Daily Papers

A major goal of unsupervised learning is to discover data representations that are useful for subsequent tasks, without access to supervised labels during training. Typically, this involves minimizing a surrogate objective, such as the negative log likelihood of a generative model, with the hope that representations useful for subsequent tasks will arise as a side effect. In this work, we propose instead to directly target later desired tasks by meta-learning an unsupervised learning rule which leads to representations useful for those tasks. Specifically, we target semi-supervised classification performance, and we meta-learn an algorithm -- an unsupervised weight update rule -- that produces representations useful for this task. Additionally, we constrain our unsupervised update rule to a be a biologically-motivated, neuron-local function, which enables it to generalize to different neural network architectures, datasets, and data modalities. We show that the meta-learned update rule produces useful features and sometimes outperforms existing unsupervised learning techniques. We further show that the meta-learned unsupervised update rule generalizes to train networks with different widths, depths, and nonlinearities. It also generalizes to train on data with randomly permuted input dimensions and even generalizes from image datasets to a text task.

We develop a method for training neural networks on Boolean data in which the values at all nodes are strictly pm 1, and the resulting models are typically equivalent to networks whose nonzero weights are also pm 1. The method replaces loss minimization with a nonconvex constraint formulation. Each node implements a Boolean threshold function (BTF), and training is expressed through a divide-and-concur decomposition into two complementary constraints: one enforces local BTF consistency between inputs, weights, and output; the other imposes architectural concurrence, equating neuron outputs with downstream inputs and enforcing weight equality across training-data instantiations of the network. The reflect-reflect-relax (RRR) projection algorithm is used to reconcile these constraints. Each BTF constraint includes a lower bound on the margin. When this bound is sufficiently large, the learned representations are provably sparse and equivalent to networks composed of simple logical gates with pm 1 weights. Across a range of tasks -- including multiplier-circuit discovery, binary autoencoding, logic-network inference, and cellular automata learning -- the method achieves exact solutions or strong generalization in regimes where standard gradient-based methods struggle. These results demonstrate that projection-based constraint satisfaction provides a viable and conceptually distinct foundation for learning in discrete neural systems, with implications for interpretability and efficient inference.

High-resolution brain imaging can now capture not just synapse locations but their molecular composition, with the cost of such mapping falling exponentially. Yet such ultrastructural data has so far told us little about local neuronal physiology - specifically, the parameters (e.g., synaptic efficacies, local conductances) that govern neural dynamics. We propose to translate molecularly annotated ultrastructure into physiology, introducing the concept of an ultrastructure-to-dynamics compiler: a learned mapping from molecularly annotated ultrastructure to simulator-ready, uncertainty-aware physiological parameters. The requirement is paired training data, with jointly acquired ultrastructure from imaging, and dynamical responses to perturbations from physiological experiments. With this data we can train models that predict local physiology directly from structure. Such a compiler would support biophysical simulations by turning anatomical maps into models of circuit dynamics, shifting structure-to-function from a descriptive program to a predictive one and opening routes to understanding neural computation and forecasting intervention effects.

Spiking Neural Networks (SNNs) are computational models inspired by the structure and dynamics of biological neuronal networks. Their event-driven nature enables them to achieve high energy efficiency, particularly when deployed on neuromorphic hardware platforms. Unlike conventional Artificial Neural Networks (ANNs), which primarily rely on layered architectures, SNNs naturally support a wide range of connectivity patterns, from traditional layered structures to small-world graphs characterized by locally dense and globally sparse connections. In this work, we introduce NeuroCoreX, an FPGA-based emulator designed for the flexible co-design and testing of SNNs. NeuroCoreX supports all-to-all connectivity, providing the capability to implement diverse network topologies without architectural restrictions. It features a biologically motivated local learning mechanism based on Spike-Timing-Dependent Plasticity (STDP). The neuron model implemented within NeuroCoreX is the Leaky Integrate-and-Fire (LIF) model, with current-based synapses facilitating spike integration and transmission . A Universal Asynchronous Receiver-Transmitter (UART) interface is provided for programming and configuring the network parameters, including neuron, synapse, and learning rule settings. Users interact with the emulator through a simple Python-based interface, streamlining SNN deployment from model design to hardware execution. NeuroCoreX is released as an open-source framework, aiming to accelerate research and development in energy-efficient, biologically inspired computing.

Backpropagation algorithm has driven the remarkable success of deep neural networks, but its lack of biological plausibility and high computational costs have motivated the ongoing search for alternative training methods. Hebbian learning has attracted considerable interest as a biologically plausible alternative to backpropagation. Nevertheless, its exclusive reliance on local information, without consideration of global task objectives, fundamentally limits its scalability. Inspired by the biological synergy between neuromodulators and local plasticity, we introduce a novel model-agnostic Global-guided Hebbian Learning (GHL) framework, which seamlessly integrates local and global information to scale up across diverse networks and tasks. In specific, the local component employs Oja's rule with competitive learning to ensure stable and effective local updates. Meanwhile, the global component introduces a sign-based signal that guides the direction of local Hebbian plasticity updates. Extensive experiments demonstrate that our method consistently outperforms existing Hebbian approaches. Notably, on large-scale network and complex datasets like ImageNet, our framework achieves the competitive results and significantly narrows the gap with standard backpropagation.

Mechanistic interpretability aims to understand the behavior of neural networks by reverse-engineering their internal computations. However, current methods struggle to find clear interpretations of neural network activations because a decomposition of activations into computational features is missing. Individual neurons or model components do not cleanly correspond to distinct features or functions. We present a novel interpretability method that aims to overcome this limitation by transforming the activations of the network into a new basis - the Local Interaction Basis (LIB). LIB aims to identify computational features by removing irrelevant activations and interactions. Our method drops irrelevant activation directions and aligns the basis with the singular vectors of the Jacobian matrix between adjacent layers. It also scales features based on their importance for downstream computation, producing an interaction graph that shows all computationally-relevant features and interactions in a model. We evaluate the effectiveness of LIB on modular addition and CIFAR-10 models, finding that it identifies more computationally-relevant features that interact more sparsely, compared to principal component analysis. However, LIB does not yield substantial improvements in interpretability or interaction sparsity when applied to language models. We conclude that LIB is a promising theory-driven approach for analyzing neural networks, but in its current form is not applicable to large language models.

The local structure of V_{2}O_{3}, an archetypal strongly correlated electron system that displays a metal-insulator transition around 160 K, has been investigated via pair distribution function (PDF) analysis of neutron and x-ray total scattering data. The rhombohedral-to-monoclinic structural phase transition manifests as an abrupt change on all length scales in the observed PDF. No monoclinic distortions of the local structure are found above the transition, although coexisting regions of phase-separated rhombohedral and monoclinic symmetry are observed between 150 K and 160 K. This lack of structural fluctuations above the transition contrasts with the known presence of magnetic fluctuations in the high-temperature state, suggesting that the lattice degree of freedom plays a secondary role behind the spin degree of freedom in the transition mechanism.

Neural network models of early sensory processing typically reduce the dimensionality of streaming input data. Such networks learn the principal subspace, in the sense of principal component analysis (PCA), by adjusting synaptic weights according to activity-dependent learning rules. When derived from a principled cost function these rules are nonlocal and hence biologically implausible. At the same time, biologically plausible local rules have been postulated rather than derived from a principled cost function. Here, to bridge this gap, we derive a biologically plausible network for subspace learning on streaming data by minimizing a principled cost function. In a departure from previous work, where cost was quantified by the representation, or reconstruction, error, we adopt a multidimensional scaling (MDS) cost function for streaming data. The resulting algorithm relies only on biologically plausible Hebbian and anti-Hebbian local learning rules. In a stochastic setting, synaptic weights converge to a stationary state which projects the input data onto the principal subspace. If the data are generated by a nonstationary distribution, the network can track the principal subspace. Thus, our result makes a step towards an algorithmic theory of neural computation.

Motivated by the celebrated discrete-time model of nervous activity outlined by McCulloch and Pitts in 1943, we propose a novel continuous-time model, the McCulloch-Pitts network (MPN), for sequence learning in spiking neural networks. Our model has a local learning rule, such that the synaptic weight updates depend only on the information directly accessible by the synapse. By exploiting asymmetry in the connections between binary neurons, we show that MPN can be trained to robustly memorize multiple spatiotemporal patterns of binary vectors, generalizing the ability of the symmetric Hopfield network to memorize static spatial patterns. In addition, we demonstrate that the model can efficiently learn sequences of binary pictures as well as generative models for experimental neural spike-train data. Our learning rule is consistent with spike-timing-dependent plasticity (STDP), thus providing a theoretical ground for the systematic design of biologically inspired networks with large and robust long-range sequence storage capacity.

The static synaptic connectivity of neuronal circuits stands in direct contrast to the dynamics of their function. As in changing community interactions, different neurons can participate actively in various combinations to effect behaviors at different times. We introduce an unsupervised approach to learn the dynamic affinities between neurons in live, behaving animals, and to reveal which communities form among neurons at different times. The inference occurs in two major steps. First, pairwise non-linear affinities between neuronal traces from brain-wide calcium activity are organized by non-negative tensor factorization (NTF). Each factor specifies which groups of neurons are most likely interacting for an inferred interval in time, and for which animals. Finally, a generative model that allows for weighted community detection is applied to the functional motifs produced by NTF to reveal a dynamic functional connectome. Since time codes the different experimental variables (e.g., application of chemical stimuli), this provides an atlas of neural motifs active during separate stages of an experiment (e.g., stimulus application or spontaneous behaviors). Results from our analysis are experimentally validated, confirming that our method is able to robustly predict causal interactions between neurons to generate behavior. Code is available at https://github.com/dyballa/dynamic-connectomes.

How neuronal circuits achieve credit assignment remains a central unsolved question in systems neuroscience. Various studies have suggested plausible solutions for back-propagating error signals through multi-layer networks. These purely functionally motivated models assume distinct neuronal compartments to represent local error signals that determine the sign of synaptic plasticity. However, this explicit error modulation is inconsistent with phenomenological plasticity models in which the sign depends primarily on postsynaptic activity. Here we show how a plausible microcircuit model and Hebbian learning rule derived within an adaptive control theory framework can resolve this discrepancy. Assuming errors are encoded in top-down dis-inhibitory synaptic afferents, we show that error-modulated learning emerges naturally at the circuit level when recurrent inhibition explicitly influences Hebbian plasticity. The same learning rule accounts for experimentally observed plasticity in the absence of inhibition and performs comparably to back-propagation of error (BP) on several non-linearly separable benchmarks. Our findings bridge the gap between functional and experimentally observed plasticity rules and make concrete predictions on inhibitory modulation of excitatory plasticity.

Deep neural networks are typically trained using global error signals that backpropagate (BP) end-to-end, which is not only biologically implausible but also suffers from the update locking problem and requires huge memory consumption. Local learning, which updates each layer independently with a gradient-isolated auxiliary network, offers a promising alternative to address the above problems. However, existing local learning methods are confronted with a large accuracy gap with the BP counterpart, particularly for large-scale networks. This is due to the weak coupling between local layers and their subsequent network layers, as there is no gradient communication across layers. To tackle this issue, we put forward an augmented local learning method, dubbed AugLocal. AugLocal constructs each hidden layer's auxiliary network by uniformly selecting a small subset of layers from its subsequent network layers to enhance their synergy. We also propose to linearly reduce the depth of auxiliary networks as the hidden layer goes deeper, ensuring sufficient network capacity while reducing the computational cost of auxiliary networks. Our extensive experiments on four image classification datasets (i.e., CIFAR-10, SVHN, STL-10, and ImageNet) demonstrate that AugLocal can effectively scale up to tens of local layers with a comparable accuracy to BP-trained networks while reducing GPU memory usage by around 40%. The proposed AugLocal method, therefore, opens up a myriad of opportunities for training high-performance deep neural networks on resource-constrained platforms.Code is available at https://github.com/ChenxiangMA/AugLocal.

Recurrent neural networks (RNNs) are widely used throughout neuroscience as models of local neural activity. Many properties of single RNNs are well characterized theoretically, but experimental neuroscience has moved in the direction of studying multiple interacting areas, and RNN theory needs to be likewise extended. We take a constructive approach towards this problem, leveraging tools from nonlinear control theory and machine learning to characterize when combinations of stable RNNs will themselves be stable. Importantly, we derive conditions which allow for massive feedback connections between interacting RNNs. We parameterize these conditions for easy optimization using gradient-based techniques, and show that stability-constrained "networks of networks" can perform well on challenging sequential-processing benchmark tasks. Altogether, our results provide a principled approach towards understanding distributed, modular function in the brain.

Understanding the inner workings of neural networks is essential for enhancing model performance and interpretability. Current research predominantly focuses on examining the connection between individual neurons and the model's final predictions. Which suffers from challenges in interpreting the internal workings of the model, particularly when neurons encode multiple unrelated features. In this paper, we propose a novel framework that transitions the focus from analyzing individual neurons to investigating groups of neurons, shifting the emphasis from neuron-output relationships to functional interaction between neurons. Our automated framework, NeurFlow, first identifies core neurons and clusters them into groups based on shared functional relationships, enabling a more coherent and interpretable view of the network's internal processes. This approach facilitates the construction of a hierarchical circuit representing neuron interactions across layers, thus improving interpretability while reducing computational costs. Our extensive empirical studies validate the fidelity of our proposed NeurFlow. Additionally, we showcase its utility in practical applications such as image debugging and automatic concept labeling, thereby highlighting its potential to advance the field of neural network explainability.

Going beyond 'dendritic democracy', we introduce a 'democracy of local processors', termed Cooperator. Here we compare their capabilities when used in permutation-invariant neural networks for reinforcement learning (RL), with machine learning algorithms based on Transformers, such as ChatGPT. Transformers are based on the long-standing conception of integrate-and-fire 'point' neurons, whereas Cooperator is inspired by recent neurobiological breakthroughs suggesting that the cellular foundations of mental life depend on context-sensitive pyramidal neurons in the neocortex which have two functionally distinct points. We show that when used for RL, an algorithm based on Cooperator learns far quicker than that based on Transformer, even while having the same number of parameters.

Training deep neural networks (DNNs) using traditional backpropagation (BP) presents challenges in terms of computational complexity and energy consumption, particularly for on-device learning where computational resources are limited. Various alternatives to BP, including random feedback alignment, forward-forward, and local classifiers, have been explored to address these challenges. These methods have their advantages, but they can encounter difficulties when dealing with intricate visual tasks or demand considerable computational resources. In this paper, we propose a novel Local Learning rule inspired by neural activity Synchronization phenomena (LLS) observed in the brain. LLS utilizes fixed periodic basis vectors to synchronize neuron activity within each layer, enabling efficient training without the need for additional trainable parameters. We demonstrate the effectiveness of LLS and its variations, LLS-M and LLS-MxM, on multiple image classification datasets, achieving accuracy comparable to BP with reduced computational complexity and minimal additional parameters. Furthermore, the performance of LLS on the Visual Wake Word (VWW) dataset highlights its suitability for on-device learning tasks, making it a promising candidate for edge hardware implementations.

The choice of activation function plays a critical role in neural networks, yet most architectures still rely on fixed, uniform activation functions across all neurons. We introduce SmartMixed, a two-phase training strategy that allows networks to learn optimal per-neuron activation functions while preserving computational efficiency at inference. In the first phase, neurons adaptively select from a pool of candidate activation functions (ReLU, Sigmoid, Tanh, Leaky ReLU, ELU, SELU) using a differentiable hard-mixture mechanism. In the second phase, each neuron's activation function is fixed according to the learned selection, resulting in a computationally efficient network that supports continued training with optimized vectorized operations. We evaluate SmartMixed on the MNIST dataset using feedforward neural networks of varying depths. The analysis shows that neurons in different layers exhibit distinct preferences for activation functions, providing insights into the functional diversity within neural architectures.

We explore the effects of various plasticity functions on assemblies of neurons. To bridge the gap between experimental and computational theories we make use of a conceptual framework, the Assembly Calculus, which is a formal system for the description of brain function based on assemblies of neurons. The Assembly Calculus includes operations for projecting, associating, and merging assemblies of neurons. Our research is focused on simulating different plasticity functions with Assembly Calculus. Our main contribution is the modification and evaluation of the projection operation. We experiment with Oja's and Spike Time-Dependent Plasticity (STDP) rules and test the effect of various hyper-parameters.

Neural networks require a careful design in order to perform properly on a given task. In particular, selecting a good activation function (possibly in a data-dependent fashion) is a crucial step, which remains an open problem in the research community. Despite a large amount of investigations, most current implementations simply select one fixed function from a small set of candidates, which is not adapted during training, and is shared among all neurons throughout the different layers. However, neither two of these assumptions can be supposed optimal in practice. In this paper, we present a principled way to have data-dependent adaptation of the activation functions, which is performed independently for each neuron. This is achieved by leveraging over past and present advances on cubic spline interpolation, allowing for local adaptation of the functions around their regions of use. The resulting algorithm is relatively cheap to implement, and overfitting is counterbalanced by the inclusion of a novel damping criterion, which penalizes unwanted oscillations from a predefined shape. Experimental results validate the proposal over two well-known benchmarks.

Why do brains have inhibitory connections? Why do deep networks have negative weights? We propose an answer from the perspective of representation capacity. We believe representing functions is the primary role of both (i) the brain in natural intelligence, and (ii) deep networks in artificial intelligence. Our answer to why there are inhibitory/negative weights is: to learn more functions. We prove that, in the absence of negative weights, neural networks with non-decreasing activation functions are not universal approximators. While this may be an intuitive result to some, to the best of our knowledge, there is no formal theory, in either machine learning or neuroscience, that demonstrates why negative weights are crucial in the context of representation capacity. Further, we provide insights on the geometric properties of the representation space that non-negative deep networks cannot represent. We expect these insights will yield a deeper understanding of more sophisticated inductive priors imposed on the distribution of weights that lead to more efficient biological and machine learning.

The informational synthesis of neural structures, processes, parameters and characteristics that allow a unified description and modeling as neural machines of natural and artificial neural systems is presented. The general informational parameters as the global quantitative measure of the neural systems computing potential as absolute and relative neural power were proposed. Neural information organizing and processing follows the way in which nature manages neural information by developing functions, functionalities and circuits related to different internal or peripheral components and also to the whole system through a non-deterministic memorization, fragmentation and aggregation of afferent and efferent information, deep neural information processing representing multiple alternations of fragmentation and aggregation stages. The relevant neural characteristics were integrated into a neural machine type model that incorporates unitary also peripheral or interface components as the central ones. The proposed approach allows overcoming the technical constraints in artificial computational implementations of neural information processes and also provides a more relevant description of natural ones.

We propose a formal mathematical model for sparse representations and active dendrites in neocortex. Our model is inspired by recent experimental findings on active dendritic processing and NMDA spikes in pyramidal neurons. These experimental and modeling studies suggest that the basic unit of pattern memory in the neocortex is instantiated by small clusters of synapses operated on by localized non-linear dendritic processes. We derive a number of scaling laws that characterize the accuracy of such dendrites in detecting activation patterns in a neuronal population under adverse conditions. We introduce the union property which shows that synapses for multiple patterns can be randomly mixed together within a segment and still lead to highly accurate recognition. We describe simulation results that provide further insight into sparse representations as well as two primary results. First we show that pattern recognition by a neuron with active dendrites can be extremely accurate and robust with high dimensional sparse inputs even when using a tiny number of synapses to recognize large patterns. Second, equations representing recognition accuracy of a dendrite predict optimal NMDA spiking thresholds under a generous set of assumptions. The prediction tightly matches NMDA spiking thresholds measured in the literature. Our model matches many of the known properties of pyramidal neurons. As such the theory provides a mathematical framework for understanding the benefits and limits of sparse representations in cortical networks.

The Spiking Neural Network (SNN) has attracted more and more attention recently. It adopts binary spike signals to transmit information. Benefitting from the information passing paradigm of SNNs, the multiplications of activations and weights can be replaced by additions, which are more energy-efficient. However, its ``Hard Reset" mechanism for the firing activity would ignore the difference among membrane potentials when the membrane potential is above the firing threshold, causing information loss. Meanwhile, quantifying the membrane potential to 0/1 spikes at the firing instants will inevitably introduce the quantization error thus bringing about information loss too. To address these problems, we propose to use the ``Soft Reset" mechanism for the supervised training-based SNNs, which will drive the membrane potential to a dynamic reset potential according to its magnitude, and Membrane Potential Rectifier (MPR) to reduce the quantization error via redistributing the membrane potential to a range close to the spikes. Results show that the SNNs with the ``Soft Reset" mechanism and MPR outperform their vanilla counterparts on both static and dynamic datasets.

Learning synaptic weights of spiking neural network (SNN) models that can reproduce target spike trains from provided neural firing data is a central problem in computational neuroscience and spike-based computing. The discovery of the optimal weight values can be posed as a supervised learning task wherein the weights of the model network are chosen to maximize the similarity between the target spike trains and the model outputs. It is still largely unknown whether optimizing spike train similarity of highly recurrent SNNs produces weight matrices similar to those of the ground truth model. To this end, we propose flexible heuristic supervised learning rules, termed Pre-Synaptic Pool Modification (PSPM), that rely on stochastic weight updates in order to produce spikes within a short window of the desired times and eliminate spikes outside of this window. PSPM improves spike train similarity for all-to-all SNNs and makes no assumption about the post-synaptic potential of the neurons or the structure of the network since no gradients are required. We test whether optimizing for spike train similarity entails the discovery of accurate weights and explore the relative contributions of local and homeostatic weight updates. Although PSPM improves similarity between spike trains, the learned weights often differ from the weights of the ground truth model, implying that connectome inference from spike data may require additional constraints on connectivity statistics. We also find that spike train similarity is sensitive to local updates, but other measures of network activity such as avalanche distributions, can be learned through synaptic homeostasis.

A basic question within the emerging field of mechanistic interpretability is the degree to which neural networks learn the same underlying mechanisms. In other words, are neural mechanisms universal across different models? In this work, we study the universality of individual neurons across GPT2 models trained from different initial random seeds, motivated by the hypothesis that universal neurons are likely to be interpretable. In particular, we compute pairwise correlations of neuron activations over 100 million tokens for every neuron pair across five different seeds and find that 1-5\% of neurons are universal, that is, pairs of neurons which consistently activate on the same inputs. We then study these universal neurons in detail, finding that they usually have clear interpretations and taxonomize them into a small number of neuron families. We conclude by studying patterns in neuron weights to establish several universal functional roles of neurons in simple circuits: deactivating attention heads, changing the entropy of the next token distribution, and predicting the next token to (not) be within a particular set.

We interpret the function of individual neurons in CLIP by automatically describing them using text. Analyzing the direct effects (i.e. the flow from a neuron through the residual stream to the output) or the indirect effects (overall contribution) fails to capture the neurons' function in CLIP. Therefore, we present the "second-order lens", analyzing the effect flowing from a neuron through the later attention heads, directly to the output. We find that these effects are highly selective: for each neuron, the effect is significant for <2% of the images. Moreover, each effect can be approximated by a single direction in the text-image space of CLIP. We describe neurons by decomposing these directions into sparse sets of text representations. The sets reveal polysemantic behavior - each neuron corresponds to multiple, often unrelated, concepts (e.g. ships and cars). Exploiting this neuron polysemy, we mass-produce "semantic" adversarial examples by generating images with concepts spuriously correlated to the incorrect class. Additionally, we use the second-order effects for zero-shot segmentation and attribute discovery in images. Our results indicate that a scalable understanding of neurons can be used for model deception and for introducing new model capabilities.

Models of neural responses to stimuli with complex spatiotemporal correlation structure often assume that neurons are only selective for a small number of linear projections of a potentially high-dimensional input. Here we explore recent modeling approaches where the neural response depends on the quadratic form of the input rather than on its linear projection, that is, the neuron is sensitive to the local covariance structure of the signal preceding the spike. To infer this quadratic dependence in the presence of arbitrary (e.g. naturalistic) stimulus distribution, we review several inference methods, focussing in particular on two information-theory-based approaches (maximization of stimulus energy or of noise entropy) and a likelihood-based approach (Bayesian spike-triggered covariance, extensions of generalized linear models). We analyze the formal connection between the likelihood-based and information-based approaches to show how they lead to consistent inference. We demonstrate the practical feasibility of these procedures by using model neurons responding to a flickering variance stimulus.

Vital to primary visual processing, retinal circuitry shows many similar structures across a very broad array of species, both vertebrate and non-vertebrate, especially functional components such as lateral inhibition. This surprisingly conservative pattern raises a question of how evolution leads to it, and whether there is any alternative that can also prompt helpful preprocessing. Here we design a method using genetic algorithm that, with many degrees of freedom, leads to architectures whose functions are similar to biological retina, as well as effective alternatives that are different in structures and functions. We compare this model to natural evolution and discuss how our framework can come into goal-driven search and sustainable enhancement of neural network models in machine learning.

Learning and decision making in the brain are key processes critical to survival, and yet are processes implemented by non-ideal biological building blocks which can impose significant error. We explore quantitatively how the brain might cope with this inherent source of error by taking advantage of two ubiquitous mechanisms, redundancy and synchronization. In particular we consider a neural process whose goal is to learn a decision function by implementing a nonlinear gradient dynamics. The dynamics, however, are assumed to be corrupted by perturbations modeling the error which might be incurred due to limitations of the biology, intrinsic neuronal noise, and imperfect measurements. We show that error, and the associated uncertainty surrounding a learned solution, can be controlled in large part by trading off synchronization strength among multiple redundant neural systems against the noise amplitude. The impact of the coupling between such redundant systems is quantified by the spectrum of the network Laplacian, and we discuss the role of network topology in synchronization and in reducing the effect of noise. A range of situations in which the mechanisms we model arise in brain science are discussed, and we draw attention to experimental evidence suggesting that cortical circuits capable of implementing the computations of interest here can be found on several scales. Finally, simulations comparing theoretical bounds to the relevant empirical quantities show that the theoretical estimates we derive can be tight.

Spiking Neural Networks (SNNs) offer energy-efficient, biologically plausible computation but suffer from non-differentiable spike generation, necessitating reliance on heuristic surrogate gradients. This paper introduces UltraLIF, a principled framework that replaces surrogate gradients with ultradiscretization, a mathematical formalism from tropical geometry providing continuous relaxations of discrete dynamics. The central insight is that the max-plus semiring underlying ultradiscretization naturally models neural threshold dynamics: the log-sum-exp function serves as a differentiable soft-maximum that converges to hard thresholding as a learnable temperature parameter eps to 0. Two neuron models are derived from distinct dynamical systems: UltraLIF from the LIF ordinary differential equation (temporal dynamics) and UltraDLIF from the diffusion equation modeling gap junction coupling across neuronal populations (spatial dynamics). Both yield fully differentiable SNNs trainable via standard backpropagation with no forward-backward mismatch. Theoretical analysis establishes pointwise convergence to classical LIF dynamics with quantitative error bounds and bounded non-vanishing gradients. Experiments on six benchmarks spanning static images, neuromorphic vision, and audio demonstrate improvements over surrogate gradient baselines, with gains most pronounced in single-timestep (T{=}1) settings on neuromorphic and temporal datasets. An optional sparsity penalty enables significant energy reduction while maintaining competitive accuracy.

Neural networks have proven to be a highly effective tool for solving complex problems in many areas of life. Recently, their importance and practical usability have further been reinforced with the advent of deep learning. One of the important conditions for the success of neural networks is the choice of an appropriate activation function introducing non-linearity into the model. Many types of these functions have been proposed in the literature in the past, but there is no single comprehensive source containing their exhaustive overview. The absence of this overview, even in our experience, leads to redundancy and the unintentional rediscovery of already existing activation functions. To bridge this gap, our paper presents an extensive survey involving 400 activation functions, which is several times larger in scale than previous surveys. Our comprehensive compilation also references these surveys; however, its main goal is to provide the most comprehensive overview and systematization of previously published activation functions with links to their original sources. The secondary aim is to update the current understanding of this family of functions.

Nowadays, neural networks act as a synonym for artificial intelligence. Present neural network models, although remarkably powerful, are inefficient both in terms of data and energy. Several alternative forms of neural networks have been proposed to address some of these problems. Specifically, spiking neural networks are suitable for efficient hardware implementations. However, effective learning algorithms for spiking networks remain elusive, although it is suspected that effective plasticity mechanisms could alleviate the problem of data efficiency. Here, we present a new framework for spiking neural networks - Spark - built upon the idea of modular design, from simple components to entire models. The aim of this framework is to provide an efficient and streamlined pipeline for spiking neural networks. We showcase this framework by solving the sparse-reward cartpole problem with simple plasticity mechanisms. We hope that a framework compatible with traditional ML pipelines may accelerate research in the area, specifically for continuous and unbatched learning, akin to the one animals exhibit.

Artificial Neural Networks (ANN) have gained significant popularity thanks to their ability to learn using the well-known backpropagation algorithm. Conversely, Spiking Neural Networks (SNNs), despite having broader capabilities than ANNs, have always posed challenges in the training phase. This paper shows a new method to perform supervised learning on SNNs, using Spike Timing Dependent Plasticity (STDP) and homeostasis, aiming at training the network to identify spatial patterns. Spatial patterns refer to spike patterns without a time component, where all spike events occur simultaneously. The method is tested using the SpiNNaker digital architecture. A SNN is trained to recognise one or multiple patterns and performance metrics are extracted to measure the performance of the network. Some considerations are drawn from the results showing that, in the case of a single trained pattern, the network behaves as the ideal detector, with 100% accuracy in detecting the trained pattern. However, as the number of trained patterns on a single network increases, the accuracy of identification is linked to the similarities between these patterns. This method of training an SNN to detect spatial patterns may be applied to pattern recognition in static images or traffic analysis in computer networks, where each network packet represents a spatial pattern. It will be stipulated that the homeostatic factor may enable the network to detect patterns with some degree of similarity, rather than only perfectly matching patterns.The principles outlined in this article serve as the fundamental building blocks for more complex systems that utilise both spatial and temporal patterns by converting specific features of input signals into spikes.One example of such a system is a computer network packet classifier, tasked with real-time identification of packet streams based on features within the packet content

Spiking neural networks (SNNs) possess energy-efficient potential due to event-based computation. However, supervised training of SNNs remains a challenge as spike activities are non-differentiable. Previous SNNs training methods can be generally categorized into two basic classes, i.e., backpropagation-like training methods and plasticity-based learning methods. The former methods are dependent on energy-inefficient real-valued computation and non-local transmission, as also required in artificial neural networks (ANNs), whereas the latter are either considered to be biologically implausible or exhibit poor performance. Hence, biologically plausible (bio-plausible) high-performance supervised learning (SL) methods for SNNs remain deficient. In this paper, we proposed a novel bio-plausible SNN model for SL based on the symmetric spike-timing dependent plasticity (sym-STDP) rule found in neuroscience. By combining the sym-STDP rule with bio-plausible synaptic scaling and intrinsic plasticity of the dynamic threshold, our SNN model implemented SL well and achieved good performance in the benchmark recognition task (MNIST dataset). To reveal the underlying mechanism of our SL model, we visualized both layer-based activities and synaptic weights using the t-distributed stochastic neighbor embedding (t-SNE) method after training and found that they were well clustered, thereby demonstrating excellent classification ability. Furthermore, to verify the robustness of our model, we trained it on another more realistic dataset (Fashion-MNIST), which also showed good performance. As the learning rules were bio-plausible and based purely on local spike events, our model could be easily applied to neuromorphic hardware for online training and may be helpful for understanding SL information processing at the synaptic level in biological neural systems.

The coding mechanism of sensory memory on the neuron scale is one of the most important questions in neuroscience. We have put forward a quantitative neural network model, which is self organized, self similar, and self adaptive, just like an ecosystem following Darwin theory. According to this model, neural coding is a mult to one mapping from objects to neurons. And the whole cerebrum is a real-time statistical Turing Machine, with powerful representing and learning ability. This model can reconcile some important disputations, such as: temporal coding versus rate based coding, grandmother cell versus population coding, and decay theory versus interference theory. And it has also provided explanations for some key questions such as memory consolidation, episodic memory, consciousness, and sentiment. Philosophical significance is indicated at last.

Biological nervous systems are created in a fundamentally different way than current artificial neural networks. Despite its impressive results in a variety of different domains, deep learning often requires considerable engineering effort to design high-performing neural architectures. By contrast, biological nervous systems are grown through a dynamic self-organizing process. In this paper, we take initial steps toward neural networks that grow through a developmental process that mirrors key properties of embryonic development in biological organisms. The growth process is guided by another neural network, which we call a Neural Developmental Program (NDP) and which operates through local communication alone. We investigate the role of neural growth on different machine learning benchmarks and different optimization methods (evolutionary training, online RL, offline RL, and supervised learning). Additionally, we highlight future research directions and opportunities enabled by having self-organization driving the growth of neural networks.

The neurons of artificial neural networks were originally invented when much less was known about biological neurons than is known today. Our work explores a modification to the core neuron unit to make it more parallel to a biological neuron. The modification is made with the knowledge that biological dendrites are not simply passive activation funnels, but also compute complex non-linear functions as they transmit activation to the cell body. The paper explores a novel system of "Perforated" backpropagation empowering the artificial neurons of deep neural networks to achieve better performance coding for the same features they coded for in the original architecture. After an initial network training phase, additional "Dendrite Nodes" are added to the network and separately trained with a different objective: to correlate their output with the remaining error of the original neurons. The trained Dendrite Nodes are then frozen, and the original neurons are further trained, now taking into account the additional error signals provided by the Dendrite Nodes. The cycle of training the original neurons and then adding and training Dendrite Nodes can be repeated several times until satisfactory performance is achieved. Our algorithm was successfully added to modern state-of-the-art PyTorch networks across multiple domains, improving upon original accuracies and allowing for significant model compression without a loss in accuracy.

Recurrent Neural Networks (RNNs) are popular models of brain function. The typical training strategy is to adjust their input-output behavior so that it matches that of the biological circuit of interest. Even though this strategy ensures that the biological and artificial networks perform the same computational task, it does not guarantee that their internal activity dynamics match. This suggests that the trained RNNs might end up performing the task employing a different internal computational mechanism, which would make them a suboptimal model of the biological circuit. In this work, we introduce a novel training strategy that allows learning not only the input-output behavior of an RNN but also its internal network dynamics, based on sparse neural recordings. We test the proposed method by training an RNN to simultaneously reproduce internal dynamics and output signals of a physiologically-inspired neural model. Specifically, this model generates the multiphasic muscle-like activity patterns typically observed during the execution of reaching movements, based on the oscillatory activation patterns concurrently observed in the motor cortex. Remarkably, we show that the reproduction of the internal dynamics is successful even when the training algorithm relies on the activities of a small subset of neurons sampled from the biological network. Furthermore, we show that training the RNNs with this method significantly improves their generalization performance. Overall, our results suggest that the proposed method is suitable for building powerful functional RNN models, which automatically capture important computational properties of the biological circuit of interest from sparse neural recordings.

Large Language Models (LLMs) possess vast amounts of knowledge within their parameters, prompting research into methods for locating and editing this knowledge. Previous work has largely focused on locating entity-related (often single-token) facts in smaller models. However, several key questions remain unanswered: (1) How can we effectively locate query-relevant neurons in decoder-only LLMs, such as Llama and Mistral? (2) How can we address the challenge of long-form (or free-form) text generation? (3) Are there localized knowledge regions in LLMs? In this study, we introduce Query-Relevant Neuron Cluster Attribution (QRNCA), a novel architecture-agnostic framework capable of identifying query-relevant neurons in LLMs. QRNCA allows for the examination of long-form answers beyond triplet facts by employing the proxy task of multi-choice question answering. To evaluate the effectiveness of our detected neurons, we build two multi-choice QA datasets spanning diverse domains and languages. Empirical evaluations demonstrate that our method outperforms baseline methods significantly. Further, analysis of neuron distributions reveals the presence of visible localized regions, particularly within different domains. Finally, we show potential applications of our detected neurons in knowledge editing and neuron-based prediction.

Many learning algorithms used as normative models in neuroscience or as candidate approaches for learning on neuromorphic chips learn by contrasting one set of network states with another. These Contrastive Learning (CL) algorithms are traditionally implemented with rigid, temporally non-local, and periodic learning dynamics that could limit the range of physical systems capable of harnessing CL. In this study, we build on recent work exploring how CL might be implemented by biological or neurmorphic systems and show that this form of learning can be made temporally local, and can still function even if many of the dynamical requirements of standard training procedures are relaxed. Thanks to a set of general theorems corroborated by numerical experiments across several CL models, our results provide theoretical foundations for the study and development of CL methods for biological and neuromorphic neural networks.

Compared with rate-based artificial neural networks, Spiking Neural Networks (SNN) provide a more biological plausible model for the brain. But how they perform supervised learning remains elusive. Inspired by recent works of Bengio et al., we propose a supervised learning algorithm based on Spike-Timing Dependent Plasticity (STDP) for a hierarchical SNN consisting of Leaky Integrate-and-fire (LIF) neurons. A time window is designed for the presynaptic neuron and only the spikes in this window take part in the STDP updating process. The model is trained on the MNIST dataset. The classification accuracy approach that of a Multilayer Perceptron (MLP) with similar architecture trained by the standard back-propagation algorithm.

It has long been known in both neuroscience and AI that ``binding'' between neurons leads to a form of competitive learning where representations are compressed in order to represent more abstract concepts in deeper layers of the network. More recently, it was also hypothesized that dynamic (spatiotemporal) representations play an important role in both neuroscience and AI. Building on these ideas, we introduce Artificial Kuramoto Oscillatory Neurons (AKOrN) as a dynamical alternative to threshold units, which can be combined with arbitrary connectivity designs such as fully connected, convolutional, or attentive mechanisms. Our generalized Kuramoto updates bind neurons together through their synchronization dynamics. We show that this idea provides performance improvements across a wide spectrum of tasks such as unsupervised object discovery, adversarial robustness, calibrated uncertainty quantification, and reasoning. We believe that these empirical results show the importance of rethinking our assumptions at the most basic neuronal level of neural representation, and in particular show the importance of dynamical representations.

In recent years, deep learning has been a revolution in the field of machine learning, for computer vision in particular. In this approach, a deep (multilayer) artificial neural network (ANN) is trained in a supervised manner using backpropagation. Huge amounts of labeled examples are required, but the resulting classification accuracy is truly impressive, sometimes outperforming humans. Neurons in an ANN are characterized by a single, static, continuous-valued activation. Yet biological neurons use discrete spikes to compute and transmit information, and the spike times, in addition to the spike rates, matter. Spiking neural networks (SNNs) are thus more biologically realistic than ANNs, and arguably the only viable option if one wants to understand how the brain computes. SNNs are also more hardware friendly and energy-efficient than ANNs, and are thus appealing for technology, especially for portable devices. However, training deep SNNs remains a challenge. Spiking neurons' transfer function is usually non-differentiable, which prevents using backpropagation. Here we review recent supervised and unsupervised methods to train deep SNNs, and compare them in terms of accuracy, but also computational cost and hardware friendliness. The emerging picture is that SNNs still lag behind ANNs in terms of accuracy, but the gap is decreasing, and can even vanish on some tasks, while the SNNs typically require much fewer operations.

Transformers are becoming increasingly popular due to their superior performance over conventional convolutional neural networks(CNNs). However, transformers usually require a much larger amount of memory to train than CNNs, which prevents their application in many low resource settings. Local learning, which divides the network into several distinct modules and trains them individually, is a promising alternative to the end-to-end (E2E) training approach to reduce the amount of memory for training and to increase parallelism. This paper is the first to apply Local Learning on transformers for this purpose. The standard CNN-based local learning method, InfoPro [32], reconstructs the input images for each module in a CNN. However, reconstructing the entire image does not generalize well. In this paper, we propose a new mechanism for each local module, where instead of reconstructing the entire image, we reconstruct its input features, generated from previous modules. We evaluate our approach on 4 commonly used datasets and 3 commonly used decoder structures on Swin-Tiny. The experiments show that our approach outperforms InfoPro-Transformer, the InfoPro with Transfomer backbone we introduced, by at up to 0.58% on CIFAR-10, CIFAR-100, STL-10 and SVHN datasets, while using up to 12% less memory. Compared to the E2E approach, we require 36% less GPU memory when the network is divided into 2 modules and 45% less GPU memory when the network is divided into 4 modules.

A long standing goal in neuroscience has been to elucidate the functional organization of the brain. Within higher visual cortex, functional accounts have remained relatively coarse, focusing on regions of interest (ROIs) and taking the form of selectivity for broad categories such as faces, places, bodies, food, or words. Because the identification of such ROIs has typically relied on manually assembled stimulus sets consisting of isolated objects in non-ecological contexts, exploring functional organization without robust a priori hypotheses has been challenging. To overcome these limitations, we introduce a data-driven approach in which we synthesize images predicted to activate a given brain region using paired natural images and fMRI recordings, bypassing the need for category-specific stimuli. Our approach -- Brain Diffusion for Visual Exploration ("BrainDiVE") -- builds on recent generative methods by combining large-scale diffusion models with brain-guided image synthesis. Validating our method, we demonstrate the ability to synthesize preferred images with appropriate semantic specificity for well-characterized category-selective ROIs. We then show that BrainDiVE can characterize differences between ROIs selective for the same high-level category. Finally we identify novel functional subdivisions within these ROIs, validated with behavioral data. These results advance our understanding of the fine-grained functional organization of human visual cortex, and provide well-specified constraints for further examination of cortical organization using hypothesis-driven methods.

Biological cortical neurons are remarkably sophisticated computational devices, temporally integrating their vast synaptic input over an intricate dendritic tree, subject to complex, nonlinearly interacting internal biological processes. A recent study proposed to characterize this complexity by fitting accurate surrogate models to replicate the input-output relationship of a detailed biophysical cortical pyramidal neuron model and discovered it needed temporal convolutional networks (TCN) with millions of parameters. Requiring these many parameters, however, could stem from a misalignment between the inductive biases of the TCN and cortical neuron's computations. In light of this, and to explore the computational implications of leaky memory units and nonlinear dendritic processing, we introduce the Expressive Leaky Memory (ELM) neuron model, a biologically inspired phenomenological model of a cortical neuron. Remarkably, by exploiting such slowly decaying memory-like hidden states and two-layered nonlinear integration of synaptic input, our ELM neuron can accurately match the aforementioned input-output relationship with under ten thousand trainable parameters. To further assess the computational ramifications of our neuron design, we evaluate it on various tasks with demanding temporal structures, including the Long Range Arena (LRA) datasets, as well as a novel neuromorphic dataset based on the Spiking Heidelberg Digits dataset (SHD-Adding). Leveraging a larger number of memory units with sufficiently long timescales, and correspondingly sophisticated synaptic integration, the ELM neuron displays substantial long-range processing capabilities, reliably outperforming the classic Transformer or Chrono-LSTM architectures on LRA, and even solving the Pathfinder-X task with over 70% accuracy (16k context length).

Deep neural networks (DNNs) have demonstrated state-of-the-art results on many pattern recognition tasks, especially vision classification problems. Understanding the inner workings of such computational brains is both fascinating basic science that is interesting in its own right - similar to why we study the human brain - and will enable researchers to further improve DNNs. One path to understanding how a neural network functions internally is to study what each of its neurons has learned to detect. One such method is called activation maximization (AM), which synthesizes an input (e.g. an image) that highly activates a neuron. Here we dramatically improve the qualitative state of the art of activation maximization by harnessing a powerful, learned prior: a deep generator network (DGN). The algorithm (1) generates qualitatively state-of-the-art synthetic images that look almost real, (2) reveals the features learned by each neuron in an interpretable way, (3) generalizes well to new datasets and somewhat well to different network architectures without requiring the prior to be relearned, and (4) can be considered as a high-quality generative method (in this case, by generating novel, creative, interesting, recognizable images).

As one of the energy-efficient alternatives of conventional neural networks (CNNs), spiking neural networks (SNNs) have gained more and more interest recently. To train the deep models, some effective batch normalization (BN) techniques are proposed in SNNs. All these BNs are suggested to be used after the convolution layer as usually doing in CNNs. However, the spiking neuron is much more complex with the spatio-temporal dynamics. The regulated data flow after the BN layer will be disturbed again by the membrane potential updating operation before the firing function, i.e., the nonlinear activation. Therefore, we advocate adding another BN layer before the firing function to normalize the membrane potential again, called MPBN. To eliminate the induced time cost of MPBN, we also propose a training-inference-decoupled re-parameterization technique to fold the trained MPBN into the firing threshold. With the re-parameterization technique, the MPBN will not introduce any extra time burden in the inference. Furthermore, the MPBN can also adopt the element-wised form, while these BNs after the convolution layer can only use the channel-wised form. Experimental results show that the proposed MPBN performs well on both popular non-spiking static and neuromorphic datasets. Our code is open-sourced at https://github.com/yfguo91/MPBN{MPBN}.

In the artificial neuron, I replace the dot product with the weighted Lehmer mean, which may emulate different cases of a generalized mean. The single neuron instance is replaced by a multiplet of neurons which have the same averaging weights. A group of outputs feed forward, in lieu of the single scalar. The generalization parameter is typically set to a different value for each neuron in the multiplet. I further extend the concept to a multiplet taken from the Gini mean. Derivatives with respect to the weight parameters and with respect to the two generalization parameters are given. Some properties of the network are investigated, showing the capacity to emulate the classical exclusive-or problem organically in two layers and perform some multiplication and division. The network can instantiate truncated power series and variants, which can be used to approximate different functions, provided that parameters are constrained. Moreover, a mean case slope score is derived that can facilitate a learning-rate novelty based on homogeneity of the selected elements. The multiplet neuron equation provides a way to segment regularization timeframes and approaches.

Partially inspired by features of computation in visual cortex, deep neural networks compute hierarchical representations of their inputs. While these networks have been highly successful in machine learning, it remains unclear to what extent they can aid our understanding of cortical function. Several groups have developed metrics that provide a quantitative comparison between representations computed by networks and representations measured in cortex. At the same time, neuroscience is well into an unprecedented phase of large-scale data collection, as evidenced by projects such as the Allen Brain Observatory. Despite the magnitude of these efforts, in a given experiment only a fraction of units are recorded, limiting the information available about the cortical representation. Moreover, only a finite number of stimuli can be shown to an animal over the course of a realistic experiment. These limitations raise the question of how and whether metrics that compare representations of deep networks are meaningful on these datasets. Here, we empirically quantify the capabilities and limitations of these metrics due to limited image presentations and neuron samples. We find that the comparison procedure is robust to different choices of stimuli set and the level of subsampling that one might expect in a large-scale brain survey with thousands of neurons. Using these results, we compare the representations measured in the Allen Brain Observatory in response to natural image presentations to deep neural network. We show that the visual cortical areas are relatively high order representations (in that they map to deeper layers of convolutional neural networks). Furthermore, we see evidence of a broad, more parallel organization rather than a sequential hierarchy, with the primary area VISp(V1) being lower order relative to the other areas.

Finding a code to unravel the population of neural responses that leads to a distinct animal behavior has been a long-standing question in the field of neuroscience. With the recent advances in machine learning, it is shown that the hierarchically Deep Neural Networks (DNNs) perform optimally in decoding unique features out of complex datasets. In this study, we utilize the power of a DNN to explore the computational principles in the mammalian brain by exploiting the Neuropixel data from Allen Brain Institute. We decode the neural responses from mouse visual cortex to predict the presented stimuli to the animal for natural (bear, trees, cheetah, etc.) and artificial (drifted gratings, orientated bars, etc.) classes. Our results indicate that neurons in mouse visual cortex encode the features of natural and artificial objects in a distinct manner, and such neural code is consistent across animals. We investigate this by applying transfer learning to train a DNN on the neural responses of a single animal and test its generalized performance across multiple animals. Within a single animal, DNN is able to decode the neural responses with as much as 100% classification accuracy. Across animals, this accuracy is reduced to 91%. This study demonstrates the potential of utilizing the DNN models as a computational framework to understand the neural coding principles in the mammalian brain.

Transformer architectures have achieved remarkable success in various domains. While efficient alternatives to Softmax Attention have been widely studied, the search for more expressive mechanisms grounded in theoretical insight-even at greater computational cost-has been relatively underexplored. In this work, we bridge this gap by proposing Local Linear Attention (LLA), a novel attention mechanism derived from nonparametric statistics through the lens of test-time regression. First, we show that LLA offers theoretical advantages over Linear and Softmax Attention for associative memory via a bias-variance trade-off analysis. Next, we address its computational challenges and propose two memory-efficient primitives to tackle the Theta(n^2 d) and Theta(n d^2) complexity. We then introduce FlashLLA, a hardware-efficient, blockwise algorithm that enables scalable and parallel computation on modern accelerators. In addition, we implement and profile a customized inference kernel that significantly reduces memory overheads. Finally, we empirically validate the advantages and limitations of LLA on test-time regression, in-context regression, associative recall and state tracking tasks. Experiment results demonstrate that LLA effectively adapts to non-stationarity, outperforming strong baselines in test-time training and in-context learning, and exhibiting promising evidence for its scalability and applicability in large-scale models. Code is available at https://github.com/Yifei-Zuo/Flash-LLA.

Neuromorphic computing with spiking neural networks is promising for energy-efficient artificial intelligence (AI) applications. However, different from humans who continually learn different tasks in a lifetime, neural network models suffer from catastrophic forgetting. How could neuronal operations solve this problem is an important question for AI and neuroscience. Many previous studies draw inspiration from observed neuroscience phenomena and propose episodic replay or synaptic metaplasticity, but they are not guaranteed to explicitly preserve knowledge for neuron populations. Other works focus on machine learning methods with more mathematical grounding, e.g., orthogonal projection on high dimensional spaces, but there is no neural correspondence for neuromorphic computing. In this work, we develop a new method with neuronal operations based on lateral connections and Hebbian learning, which can protect knowledge by projecting activity traces of neurons into an orthogonal subspace so that synaptic weight update will not interfere with old tasks. We show that Hebbian and anti-Hebbian learning on recurrent lateral connections can effectively extract the principal subspace of neural activities and enable orthogonal projection. This provides new insights into how neural circuits and Hebbian learning can help continual learning, and also how the concept of orthogonal projection can be realized in neuronal systems. Our method is also flexible to utilize arbitrary training methods based on presynaptic activities/traces. Experiments show that our method consistently solves forgetting for spiking neural networks with nearly zero forgetting under various supervised training methods with different error propagation approaches, and outperforms previous approaches under various settings. Our method can pave a solid path for building continual neuromorphic computing systems.

In this paper, we propose a novel model-parallel learning method, called local critic training, which trains neural networks using additional modules called local critic networks. The main network is divided into several layer groups and each layer group is updated through error gradients estimated by the corresponding local critic network. We show that the proposed approach successfully decouples the update process of the layer groups for both convolutional neural networks (CNNs) and recurrent neural networks (RNNs). In addition, we demonstrate that the proposed method is guaranteed to converge to a critical point. We also show that trained networks by the proposed method can be used for structural optimization. Experimental results show that our method achieves satisfactory performance, reduces training time greatly, and decreases memory consumption per machine. Code is available at https://github.com/hjdw2/Local-critic-training.

Instance segmentation of neurons in volumetric light microscopy images of nervous systems enables groundbreaking research in neuroscience by facilitating joint functional and morphological analyses of neural circuits at cellular resolution. Yet said multi-neuron light microscopy data exhibits extremely challenging properties for the task of instance segmentation: Individual neurons have long-ranging, thin filamentous and widely branching morphologies, multiple neurons are tightly inter-weaved, and partial volume effects, uneven illumination and noise inherent to light microscopy severely impede local disentangling as well as long-range tracing of individual neurons. These properties reflect a current key challenge in machine learning research, namely to effectively capture long-range dependencies in the data. While respective methodological research is buzzing, to date methods are typically benchmarked on synthetic datasets. To address this gap, we release the FlyLight Instance Segmentation Benchmark (FISBe) dataset, the first publicly available multi-neuron light microscopy dataset with pixel-wise annotations. In addition, we define a set of instance segmentation metrics for benchmarking that we designed to be meaningful with regard to downstream analyses. Lastly, we provide three baselines to kick off a competition that we envision to both advance the field of machine learning regarding methodology for capturing long-range data dependencies, and facilitate scientific discovery in basic neuroscience.

State-of-the-art systems neuroscience experiments yield large-scale multimodal data, and these data sets require new tools for analysis. Inspired by the success of large pretrained models in vision and language domains, we reframe the analysis of large-scale, cellular-resolution neuronal spiking data into an autoregressive spatiotemporal generation problem. Neuroformer is a multimodal, multitask generative pretrained transformer (GPT) model that is specifically designed to handle the intricacies of data in systems neuroscience. It scales linearly with feature size, can process an arbitrary number of modalities, and is adaptable to downstream tasks, such as predicting behavior. We first trained Neuroformer on simulated datasets, and found that it both accurately predicted simulated neuronal circuit activity, and also intrinsically inferred the underlying neural circuit connectivity, including direction. When pretrained to decode neural responses, the model predicted the behavior of a mouse with only few-shot fine-tuning, suggesting that the model begins learning how to do so directly from the neural representations themselves, without any explicit supervision. We used an ablation study to show that joint training on neuronal responses and behavior boosted performance, highlighting the model's ability to associate behavioral and neural representations in an unsupervised manner. These findings show that Neuroformer can analyze neural datasets and their emergent properties, informing the development of models and hypotheses associated with the brain.

Neural populations exhibit latent dynamical structures that drive time-evolving spiking activities, motivating the search for models that capture both intrinsic network dynamics and external unobserved influences. In this work, we introduce LangevinFlow, a sequential Variational Auto-Encoder where the time evolution of latent variables is governed by the underdamped Langevin equation. Our approach incorporates physical priors -- such as inertia, damping, a learned potential function, and stochastic forces -- to represent both autonomous and non-autonomous processes in neural systems. Crucially, the potential function is parameterized as a network of locally coupled oscillators, biasing the model toward oscillatory and flow-like behaviors observed in biological neural populations. Our model features a recurrent encoder, a one-layer Transformer decoder, and Langevin dynamics in the latent space. Empirically, our method outperforms state-of-the-art baselines on synthetic neural populations generated by a Lorenz attractor, closely matching ground-truth firing rates. On the Neural Latents Benchmark (NLB), the model achieves superior held-out neuron likelihoods (bits per spike) and forward prediction accuracy across four challenging datasets. It also matches or surpasses alternative methods in decoding behavioral metrics such as hand velocity. Overall, this work introduces a flexible, physics-inspired, high-performing framework for modeling complex neural population dynamics and their unobserved influences.

Unsupervised learning of hierarchical representations has been one of the most vibrant research directions in deep learning during recent years. In this work we study biologically inspired unsupervised strategies in neural networks based on local Hebbian learning. We propose new mechanisms to extend the Bayesian Confidence Propagating Neural Network (BCPNN) architecture, and demonstrate their capability for unsupervised learning of salient hidden representations when tested on the MNIST dataset.

Exposing meaningful and interpretable neural interactions is critical to understanding neural circuits. Inferred neural interactions from neural signals primarily reflect functional interactions. In a long experiment, subject animals may experience different stages defined by the experiment, stimuli, or behavioral states, and hence functional interactions can change over time. To model dynamically changing functional interactions, prior work employs state-switching generalized linear models with hidden Markov models (i.e., HMM-GLMs). However, we argue they lack biological plausibility, as functional interactions are shaped and confined by the underlying anatomical connectome. Here, we propose a novel prior-informed state-switching GLM. We introduce both a Gaussian prior and a one-hot prior over the GLM in each state. The priors are learnable. We will show that the learned prior should capture the state-constant interaction, shedding light on the underlying anatomical connectome and revealing more likely physical neuron interactions. The state-dependent interaction modeled by each GLM offers traceability to capture functional variations across multiple brain states. Our methods effectively recover true interaction structures in simulated data, achieve the highest predictive likelihood with real neural datasets, and render interaction structures and hidden states more interpretable when applied to real neural data.

Training neural networks involves solving large-scale non-convex optimization problems. This task has long been believed to be extremely difficult, with fear of local minima and other obstacles motivating a variety of schemes to improve optimization, such as unsupervised pretraining. However, modern neural networks are able to achieve negligible training error on complex tasks, using only direct training with stochastic gradient descent. We introduce a simple analysis technique to look for evidence that such networks are overcoming local optima. We find that, in fact, on a straight path from initialization to solution, a variety of state of the art neural networks never encounter any significant obstacles.

The demand for low-power inference and training of deep neural networks (DNNs) on edge devices has intensified the need for algorithms that are both scalable and energy-efficient. While spiking neural networks (SNNs) allow for efficient inference by processing complex spatio-temporal dynamics in an event-driven fashion, training them on resource-constrained devices remains challenging due to the high computational and memory demands of conventional error backpropagation (BP)-based approaches. In this work, we draw inspiration from biological mechanisms such as eligibility traces, spike-timing-dependent plasticity, and neural activity synchronization to introduce TESS, a temporally and spatially local learning rule for training SNNs. Our approach addresses both temporal and spatial credit assignments by relying solely on locally available signals within each neuron, thereby allowing computational and memory overheads to scale linearly with the number of neurons, independently of the number of time steps. Despite relying on local mechanisms, we demonstrate performance comparable to the backpropagation through time (BPTT) algorithm, within sim1.4 accuracy points on challenging computer vision scenarios relevant at the edge, such as the IBM DVS Gesture dataset, CIFAR10-DVS, and temporal versions of CIFAR10, and CIFAR100. Being able to produce comparable performance to BPTT while keeping low time and memory complexity, TESS enables efficient and scalable on-device learning at the edge.

Spiking neural networks have significant potential utility in robotics due to their high energy efficiency on specialized hardware, but proof-of-concept implementations have not yet typically achieved competitive performance or capability with conventional approaches. In this paper, we tackle one of the key practical challenges of scalability by introducing a novel modular ensemble network approach, where compact, localized spiking networks each learn and are solely responsible for recognizing places in a local region of the environment only. This modular approach creates a highly scalable system. However, it comes with a high-performance cost where a lack of global regularization at deployment time leads to hyperactive neurons that erroneously respond to places outside their learned region. Our second contribution introduces a regularization approach that detects and removes these problematic hyperactive neurons during the initial environmental learning phase. We evaluate this new scalable modular system on benchmark localization datasets Nordland and Oxford RobotCar, with comparisons to standard techniques NetVLAD, DenseVLAD, and SAD, and a previous spiking neural network system. Our system substantially outperforms the previous SNN system on its small dataset, but also maintains performance on 27 times larger benchmark datasets where the operation of the previous system is computationally infeasible, and performs competitively with the conventional localization systems.

Large Language Models (LLMs) are composed of neurons that exhibit various behaviors and roles, which become increasingly diversified as models scale. Recent studies have revealed that not all neurons are active across different datasets, and this sparsity correlates positively with the task-specific ability, leading to advancements in model pruning and training efficiency. Traditional fine-tuning methods engage all parameters of LLMs, which is computationally expensive and may not be necessary. In contrast, Parameter-Efficient Fine-Tuning (PEFT) approaches aim to minimize the number of trainable parameters, yet they still operate at a relatively macro scale (e.g., layer-level). We introduce Neuron-Level Fine-Tuning (NeFT), a novel approach that refines the granularity of parameter training down to the individual neuron, enabling more precise and computationally efficient model updates. The experimental results show that NeFT not only exceeded the performance of full-parameter fine-tuning and PEFT but also provided insights into the analysis of neurons.

In complex systems, we often observe complex global behavior emerge from a collection of agents interacting with each other in their environment, with each individual agent acting only on locally available information, without knowing the full picture. Such systems have inspired development of artificial intelligence algorithms in areas such as swarm optimization and cellular automata. Motivated by the emergence of collective behavior from complex cellular systems, we build systems that feed each sensory input from the environment into distinct, but identical neural networks, each with no fixed relationship with one another. We show that these sensory networks can be trained to integrate information received locally, and through communication via an attention mechanism, can collectively produce a globally coherent policy. Moreover, the system can still perform its task even if the ordering of its inputs is randomly permuted several times during an episode. These permutation invariant systems also display useful robustness and generalization properties that are broadly applicable. Interactive demo and videos of our results: https://attentionneuron.github.io/

We analyze a family of large language models in such a lightweight manner that can be done on a single GPU. Specifically, we focus on the OPT family of models ranging from 125m to 66b parameters and rely only on whether an FFN neuron is activated or not. First, we find that the early part of the network is sparse and represents many discrete features. Here, many neurons (more than 70% in some layers of the 66b model) are "dead", i.e. they never activate on a large collection of diverse data. At the same time, many of the alive neurons are reserved for discrete features and act as token and n-gram detectors. Interestingly, their corresponding FFN updates not only promote next token candidates as could be expected, but also explicitly focus on removing the information about triggering them tokens, i.e., current input. To the best of our knowledge, this is the first example of mechanisms specialized at removing (rather than adding) information from the residual stream. With scale, models become more sparse in a sense that they have more dead neurons and token detectors. Finally, some neurons are positional: them being activated or not depends largely (or solely) on position and less so (or not at all) on textual data. We find that smaller models have sets of neurons acting as position range indicators while larger models operate in a less explicit manner.

We propose a novel algorithm called Backpropagation Neural Tree (BNeuralT), which is a stochastic computational dendritic tree. BNeuralT takes random repeated inputs through its leaves and imposes dendritic nonlinearities through its internal connections like a biological dendritic tree would do. Considering the dendritic-tree like plausible biological properties, BNeuralT is a single neuron neural tree model with its internal sub-trees resembling dendritic nonlinearities. BNeuralT algorithm produces an ad hoc neural tree which is trained using a stochastic gradient descent optimizer like gradient descent (GD), momentum GD, Nesterov accelerated GD, Adagrad, RMSprop, or Adam. BNeuralT training has two phases, each computed in a depth-first search manner: the forward pass computes neural tree's output in a post-order traversal, while the error backpropagation during the backward pass is performed recursively in a pre-order traversal. A BNeuralT model can be considered a minimal subset of a neural network (NN), meaning it is a "thinned" NN whose complexity is lower than an ordinary NN. Our algorithm produces high-performing and parsimonious models balancing the complexity with descriptive ability on a wide variety of machine learning problems: classification, regression, and pattern recognition.

Parameter-efficient fine-tuning (PEFT) methods such as adapt large pretrained models by adding small weight-space updates. While effective, weight deltas are hard to interpret mechanistically, and they do not directly expose which internal computations are reused versus bypassed for a new task. We explore an alternative view inspired by neuromodulation: adaptation as a change in mode -- selecting and rescaling existing computations -- rather than rewriting the underlying weights. We propose , a simple activation-space PEFT technique that freezes base weights and learns per-neuron thresholds and gains. During training, a smooth gate decides whether a neuron's activation participates; at inference the gate can be hardened to yield explicit conditional computation and neuron-level attributions. As a proof of concept, we study ``mode specialization'' on MNIST (0^circ) versus rotated MNIST (45^circ). We pretrain a small MLP on a 50/50 mixture (foundation), freeze its weights, and then specialize to the rotated mode using . Across seeds, improves rotated accuracy over the frozen baseline while using only a few hundred trainable parameters per layer, and exhibits partial activation sparsity (a minority of units strongly active). Compared to , trades some accuracy for substantially fewer trainable parameters and a more interpretable ``which-neurons-fire'' mechanism. We discuss limitations, including reduced expressivity when the frozen base lacks features needed for the target mode.

Diffusion models have exhibited impressive prowess in the text-to-image task. Recent methods add image-level structure controls, e.g., edge and depth maps, to manipulate the generation process together with text prompts to obtain desired images. This controlling process is globally operated on the entire image, which limits the flexibility of control regions. In this paper, we explore a novel and practical task setting: local control. It focuses on controlling specific local region according to user-defined image conditions, while the remaining regions are only conditioned by the original text prompt. However, it is non-trivial to achieve local conditional controlling. The naive manner of directly adding local conditions may lead to the local control dominance problem, which forces the model to focus on the controlled region and neglect object generation in other regions. To mitigate this problem, we propose Regional Discriminate Loss to update the noised latents, aiming at enhanced object generation in non-control regions. Furthermore, the proposed Focused Token Response suppresses weaker attention scores which lack the strongest response to enhance object distinction and reduce duplication. Lastly, we adopt Feature Mask Constraint to reduce quality degradation in images caused by information differences across the local control region. All proposed strategies are operated at the inference stage. Extensive experiments demonstrate that our method can synthesize high-quality images aligned with the text prompt under local control conditions.

Vision tasks are characterized by the properties of locality and translation invariance. The superior performance of convolutional neural networks (CNNs) on these tasks is widely attributed to the inductive bias of locality and weight sharing baked into their architecture. Existing attempts to quantify the statistical benefits of these biases in CNNs over locally connected convolutional neural networks (LCNs) and fully connected neural networks (FCNs) fall into one of the following categories: either they disregard the optimizer and only provide uniform convergence upper bounds with no separating lower bounds, or they consider simplistic tasks that do not truly mirror the locality and translation invariance as found in real-world vision tasks. To address these deficiencies, we introduce the Dynamic Signal Distribution (DSD) classification task that models an image as consisting of k patches, each of dimension d, and the label is determined by a d-sparse signal vector that can freely appear in any one of the k patches. On this task, for any orthogonally equivariant algorithm like gradient descent, we prove that CNNs require O(k+d) samples, whereas LCNs require Omega(kd) samples, establishing the statistical advantages of weight sharing in translation invariant tasks. Furthermore, LCNs need O(k(k+d)) samples, compared to Omega(k^2d) samples for FCNs, showcasing the benefits of locality in local tasks. Additionally, we develop information theoretic tools for analyzing randomized algorithms, which may be of interest for statistical research.

Hopfield neural networks are a possible basis for modelling associative memory in living organisms. After summarising previous studies in the field, we take a new look at learning rules, exhibiting them as descent-type algorithms for various cost functions. We also propose several new cost functions suitable for learning. We discuss the role of biases (the external inputs) in the learning process in Hopfield networks. Furthermore, we apply Newtons method for learning memories, and experimentally compare the performances of various learning rules. Finally, to add to the debate whether allowing connections of a neuron to itself enhances memory capacity, we numerically investigate the effects of self coupling. Keywords: Hopfield Networks, associative memory, content addressable memory, learning rules, gradient descent, attractor networks

Growing evidence indicates that only a sparse subset from a pool of sensory neurons is active for the encoding of visual stimuli at any instant in time. Traditionally, to replicate such biological sparsity, generative models have been using the ell_1 norm as a penalty due to its convexity, which makes it amenable to fast and simple algorithmic solvers. In this work, we use biological vision as a test-bed and show that the soft thresholding operation associated to the use of the ell_1 norm is highly suboptimal compared to other functions suited to approximating ell_q with 0 leq q < 1 (including recently proposed Continuous Exact relaxations), both in terms of performance and in the production of features that are akin to signatures of the primary visual cortex. We show that ell_1 sparsity produces a denser code or employs a pool with more neurons, i.e. has a higher degree of overcompleteness, in order to maintain the same reconstruction error as the other methods considered. For all the penalty functions tested, a subset of the neurons develop orientation selectivity similarly to V1 neurons. When their code is sparse enough, the methods also develop receptive fields with varying functionalities, another signature of V1. Compared to other methods, soft thresholding achieves this level of sparsity at the expense of much degraded reconstruction performance, that more likely than not is not acceptable in biological vision. Our results indicate that V1 uses a sparsity inducing regularization that is closer to the ell_0 pseudo-norm rather than to the ell_1 norm.

Prior studies on the emergence in large models have primarily focused on how the functional capabilities of large language models (LLMs) scale with model size. Our research, however, transcends this traditional paradigm, aiming to deepen our understanding of the emergence within LLMs by placing a special emphasis not just on the model size but more significantly on the complex behavior of neuron interactions during the training process. By introducing the concepts of "self-organization" and "multifractal analysis," we explore how neuron interactions dynamically evolve during training, leading to "emergence," mirroring the phenomenon in natural systems where simple micro-level interactions give rise to complex macro-level behaviors. To quantitatively analyze the continuously evolving interactions among neurons in large models during training, we propose the Neuron-based Multifractal Analysis (NeuroMFA). Utilizing NeuroMFA, we conduct a comprehensive examination of the emergent behavior in LLMs through the lens of both model size and training process, paving new avenues for research into the emergence in large models.

Deep neural networks conventionally employ end-to-end backpropagation for their training process, which lacks biological credibility and triggers a locking dilemma during network parameter updates, leading to significant GPU memory use. Supervised local learning, which segments the network into multiple local blocks updated by independent auxiliary networks. However, these methods cannot replace end-to-end training due to lower accuracy, as gradients only propagate within their local block, creating a lack of information exchange between blocks. To address this issue and establish information transfer across blocks, we propose a Momentum Auxiliary Network (MAN) that establishes a dynamic interaction mechanism. The MAN leverages an exponential moving average (EMA) of the parameters from adjacent local blocks to enhance information flow. This auxiliary network, updated through EMA, helps bridge the informational gap between blocks. Nevertheless, we observe that directly applying EMA parameters has certain limitations due to feature discrepancies among local blocks. To overcome this, we introduce learnable biases, further boosting performance. We have validated our method on four image classification datasets (CIFAR-10, STL-10, SVHN, ImageNet), attaining superior performance and substantial memory savings. Notably, our method can reduce GPU memory usage by more than 45\% on the ImageNet dataset compared to end-to-end training, while achieving higher performance. The Momentum Auxiliary Network thus offers a new perspective for supervised local learning. Our code is available at: https://github.com/JunhaoSu0/MAN.

The precise timing of spikes emitted by neurons plays a crucial role in shaping the response of efferent biological neurons. This temporal dimension of neural activity holds significant importance in understanding information processing in neurobiology, especially for the performance of neuromorphic hardware, such as event-based cameras. Nonetheless, many artificial neural models disregard this critical temporal dimension of neural activity. In this study, we present a model designed to efficiently detect temporal spiking motifs using a layer of spiking neurons equipped with heterogeneous synaptic delays. Our model capitalizes on the diverse synaptic delays present on the dendritic tree, enabling specific arrangements of temporally precise synaptic inputs to synchronize upon reaching the basal dendritic tree. We formalize this process as a time-invariant logistic regression, which can be trained using labeled data. To demonstrate its practical efficacy, we apply the model to naturalistic videos transformed into event streams, simulating the output of the biological retina or event-based cameras. To evaluate the robustness of the model in detecting visual motion, we conduct experiments by selectively pruning weights and demonstrate that the model remains efficient even under significantly reduced workloads. In conclusion, by providing a comprehensive, event-driven computational building block, the incorporation of heterogeneous delays has the potential to greatly improve the performance of future spiking neural network algorithms, particularly in the context of neuromorphic chips.

The brain understands the external world through an internal model that generates predictions and refines them based on prediction errors. A complete prediction specifies what will happen, when it will happen, and with what probability, which we refer to as a "prediction object". Existing models typically capture only what and when, omit probabilities, and rely on biologically-implausible algorithms. Here we show that a single population of spiking neurons can jointly encode the prediction object through a biologically grounded learning mechanism. We implement a heterogeneous Izhikevich spiking reservoir with readouts trained by an error-modulated, attention-gated three-factor Hebbian rule and test it on a novel paradigm that controls both the timing and probability of upcoming stimuli. By integrating real-time learning of "when" with offline consolidation of "what", the model encodes the complete prediction object, firing at the correct times with magnitudes proportional to the probabilities. Critically, it rapidly adapts to changes in both stimulus timing and probability, an ability that global least-squares methods such as FORCE lack without explicit resets. During learning, the model self-organizes its readout weights into near-orthogonal subspaces for "what" and "when," showing that multiplexed encoding arises naturally from generic recurrent dynamics under local, error-gated modulation. These results challenge the view that "what" and "when" predictions require separate modules, suggesting instead that mixed selectivity within shared populations supports flexible predictive cognition. The model also predicts phase-specific neuromodulation and overlapping neural subspaces, offering a parsimonious alternative to hierarchical predictive-coding accounts.

We study the problem of learning a single neuron with respect to the L_2^2-loss in the presence of adversarial label noise. We give an efficient algorithm that, for a broad family of activations including ReLUs, approximates the optimal L_2^2-error within a constant factor. Our algorithm applies under much milder distributional assumptions compared to prior work. The key ingredient enabling our results is a novel connection to local error bounds from optimization theory.

The deep neural nets of modern artificial intelligence (AI) have not achieved defining features of biological intelligence, including abstraction, causal learning, and energy-efficiency. While scaling to larger models has delivered performance improvements for current applications, more brain-like capacities may demand new theories, models, and methods for designing artificial learning systems. Here, we argue that this opportunity to reassess insights from the brain should stimulate cooperation between AI research and theory-driven computational neuroscience (CN). To motivate a brain basis of neural computation, we present a dynamical view of intelligence from which we elaborate concepts of sparsity in network structure, temporal dynamics, and interactive learning. In particular, we suggest that temporal dynamics, as expressed through neural synchrony, nested oscillations, and flexible sequences, provide a rich computational layer for reading and updating hierarchical models distributed in long-term memory networks. Moreover, embracing agent-centered paradigms in AI and CN will accelerate our understanding of the complex dynamics and behaviors that build useful world models. A convergence of AI/CN theories and objectives will reveal dynamical principles of intelligence for brains and engineered learning systems. This article was inspired by our symposium on dynamical neuroscience and machine learning at the 6th Annual US/NIH BRAIN Initiative Investigators Meeting.

Artificial neural networks for motor control usually adopt generic architectures like fully connected MLPs. While general, these tabula rasa architectures rely on large amounts of experience to learn, are not easily transferable to new bodies, and have internal dynamics that are difficult to interpret. In nature, animals are born with highly structured connectivity in their nervous systems shaped by evolution; this innate circuitry acts synergistically with learning mechanisms to provide inductive biases that enable most animals to function well soon after birth and learn efficiently. Convolutional networks inspired by visual circuitry have encoded useful biases for vision. However, it is unknown the extent to which ANN architectures inspired by neural circuitry can yield useful biases for other AI domains. In this work, we ask what advantages biologically inspired ANN architecture can provide in the domain of motor control. Specifically, we translate C. elegans locomotion circuits into an ANN model controlling a simulated Swimmer agent. On a locomotion task, our architecture achieves good initial performance and asymptotic performance comparable with MLPs, while dramatically improving data efficiency and requiring orders of magnitude fewer parameters. Our architecture is interpretable and transfers to new body designs. An ablation analysis shows that constrained excitation/inhibition is crucial for learning, while weight initialization contributes to good initial performance. Our work demonstrates several advantages of biologically inspired ANN architecture and encourages future work in more complex embodied control.

Advancements in LLMs have recently unveiled challenges tied to computational efficiency and continual scalability due to their requirements of huge parameters, making the applications and evolution of these models on devices with limited computation resources and scenarios requiring various abilities increasingly cumbersome. Inspired by modularity within the human brain, there is a growing tendency to decompose LLMs into numerous functional modules, allowing for inference with part of modules and dynamic assembly of modules to tackle complex tasks, such as mixture-of-experts. To highlight the inherent efficiency and composability of the modular approach, we coin the term brick to represent each functional module, designating the modularized structure as configurable foundation models. In this paper, we offer a comprehensive overview and investigation of the construction, utilization, and limitation of configurable foundation models. We first formalize modules into emergent bricks - functional neuron partitions that emerge during the pre-training phase, and customized bricks - bricks constructed via additional post-training to improve the capabilities and knowledge of LLMs. Based on diverse functional bricks, we further present four brick-oriented operations: retrieval and routing, merging, updating, and growing. These operations allow for dynamic configuration of LLMs based on instructions to handle complex tasks. To verify our perspective, we conduct an empirical analysis on widely-used LLMs. We find that the FFN layers follow modular patterns with functional specialization of neurons and functional neuron partitions. Finally, we highlight several open issues and directions for future research. Overall, this paper aims to offer a fresh modular perspective on existing LLM research and inspire the future creation of more efficient and scalable foundational models.

Large language models (LLMs) demonstrate remarkable performance across a spectrum of languages. In this work, we delve into the question: How do LLMs handle multilingualism? We introduce a framework that depicts LLMs' processing of multilingual inputs: In the first several layers, LLMs understand the question, converting multilingual inputs into English to facilitate the task-solving phase. In the intermediate layers, LLMs engage in problem-solving by thinking in English and incorporating multilingual knowledge to obtain factual content, leveraging the self-attention and feed-forward structures, respectively. In the last several layers, LLMs generate responses that align with the original language of the query. In addition, we investigate the existence of language-specific neurons when processing a certain language. To detect neurons activated by the input language, even without labels, we innovatively design a Parallel Language specific Neuron Detection (PLND) method that effectively measures the significance of neurons when handling multilingual inputs. By comprehensive ablation analysis through deactivating neurons of different layers and structures, we verify the framework that we propose. Additionally, we demonstrate that we can utilize such a framework to effectively enhance the multilingual ability with much less training effort.

Within the complex neuroarchitecture of the brain, astrocytes play crucial roles in development, structure, and metabolism. These cells regulate neural activity through tripartite synapses, directly impacting cognitive processes such as learning and memory. Despite the growing recognition of astrocytes' significance, traditional Spiking Neural Network (SNN) models remain predominantly neuron-centric, overlooking the profound influence of astrocytes on neural dynamics. Inspired by these biological insights, we have developed an Astrocyte-Modulated Spiking Unit (AM-SU), an innovative framework that integrates neuron-astrocyte interactions into the computational paradigm, demonstrating wide applicability across various hardware platforms. Our Astrocyte-Modulated Spiking Neural Network (AstroSNN) exhibits exceptional performance in tasks involving memory retention and natural language generation, particularly in handling long-term dependencies and complex linguistic structures. The design of AstroSNN not only enhances its biological authenticity but also introduces novel computational dynamics, enabling more effective processing of complex temporal dependencies. Furthermore, AstroSNN shows low latency, high throughput, and reduced memory usage in practical applications, making it highly suitable for resource-constrained environments. By successfully integrating astrocytic dynamics into intelligent neural networks, our work narrows the gap between biological plausibility and neural modeling, laying the groundwork for future biologically-inspired neural computing research that includes both neurons and astrocytes.

Large Vision-Language Models (LVLMs) generate contextually relevant responses by jointly interpreting visual and textual inputs. However, our finding reveals they often mistakenly perceive text inputs lacking visual evidence as being part of the image, leading to erroneous responses. In light of this finding, we probe whether LVLMs possess an internal capability to determine if textual concepts are grounded in the image, and discover a specific subset of Feed-Forward Network (FFN) neurons, termed Visual Absence-aware (VA) neurons, that consistently signal the visual absence through a distinctive activation pattern. Leveraging these patterns, we develop a detection module that systematically classifies whether an input token is visually grounded. Guided by its prediction, we propose a method to refine the outputs by reinterpreting question prompts or replacing the detected absent tokens during generation. Extensive experiments show that our method effectively mitigates the models' tendency to falsely presume the visual presence of text input and its generality across various LVLMs.

Large language models (LLMs) exhibit remarkable capabilities on not just language tasks, but also various tasks that are not linguistic in nature, such as logical reasoning and social inference. In the human brain, neuroscience has identified a core language system that selectively and causally supports language processing. We here ask whether similar specialization for language emerges in LLMs. We identify language-selective units within 18 popular LLMs, using the same localization approach that is used in neuroscience. We then establish the causal role of these units by demonstrating that ablating LLM language-selective units -- but not random units -- leads to drastic deficits in language tasks. Correspondingly, language-selective LLM units are more aligned to brain recordings from the human language system than random units. Finally, we investigate whether our localization method extends to other cognitive domains: while we find specialized networks in some LLMs for reasoning and social capabilities, there are substantial differences among models. These findings provide functional and causal evidence for specialization in large language models, and highlight parallels with the functional organization in the brain.

We present a deep neural-network model for lifelong learning inspired by several forms of neuroplasticity. The neural network develops continuously in response to signals from the environment. In the beginning, the network is a blank slate with no nodes at all. It develops according to four rules: (i) expansion, which adds new nodes to memorize new input combinations; (ii) generalization, which adds new nodes that generalize from existing ones; (iii) forgetting, which removes nodes that are of relatively little use; and (iv) backpropagation, which fine-tunes the network parameters. We analyze the model from the perspective of accuracy, energy efficiency, and versatility and compare it to other network models, finding better performance in several cases.

Sensory systems across all modalities and species exhibit adaptation to continuously changing input statistics. Individual neurons have been shown to modulate their response gains so as to maximize information transmission in different stimulus contexts. Experimental measurements have revealed additional, nuanced sensory adaptation effects including changes in response maxima and minima, tuning curve repulsion from the adapter stimulus, and stimulus-driven response decorrelation. Existing explanations of these phenomena rely on changes in inter-neuronal synaptic efficacy, which, while more flexible, are unlikely to operate as rapidly or reversibly as single neuron gain modulations. Using published V1 population adaptation data, we show that propagation of single neuron gain changes in a recurrent network is sufficient to capture the entire set of observed adaptation effects. We propose a novel adaptive efficient coding objective with which single neuron gains are modulated, maximizing the fidelity of the stimulus representation while minimizing overall activity in the network. From this objective, we analytically derive a set of gains that optimize the trade-off between preserving information about the stimulus and conserving metabolic resources. Our model generalizes well-established concepts of single neuron adaptive gain control to recurrent populations, and parsimoniously explains experimental adaptation data.

We find arithmetic ability resides within a limited number of attention heads, with each head specializing in distinct operations. To delve into the reason, we introduce the Comparative Neuron Analysis (CNA) method, which identifies an internal logic chain consisting of four distinct stages from input to prediction: feature enhancing with shallow FFN neurons, feature transferring by shallow attention layers, feature predicting by arithmetic heads, and prediction enhancing among deep FFN neurons. Moreover, we identify the human-interpretable FFN neurons within both feature-enhancing and feature-predicting stages. These findings lead us to investigate the mechanism of LoRA, revealing that it enhances prediction probabilities by amplifying the coefficient scores of FFN neurons related to predictions. Finally, we apply our method in model pruning for arithmetic tasks and model editing for reducing gender bias. Code is on https://github.com/zepingyu0512/arithmetic-mechanism.

Neural architectures that learn potential energy surfaces from molecular data have undergone fast improvement in recent years. A key driver of this success is the Message Passing Neural Network (MPNN) paradigm. Its favorable scaling with system size partly relies upon a spatial distance limit on messages. While this focus on locality is a useful inductive bias, it also impedes the learning of long-range interactions such as electrostatics and van der Waals forces. To address this drawback, we propose Ewald message passing: a nonlocal Fourier space scheme which limits interactions via a cutoff on frequency instead of distance, and is theoretically well-founded in the Ewald summation method. It can serve as an augmentation on top of existing MPNN architectures as it is computationally inexpensive and agnostic to architectural details. We test the approach with four baseline models and two datasets containing diverse periodic (OC20) and aperiodic structures (OE62). We observe robust improvements in energy mean absolute errors across all models and datasets, averaging 10% on OC20 and 16% on OE62. Our analysis shows an outsize impact of these improvements on structures with high long-range contributions to the ground truth energy.

Do large language models (LLMs) solve reasoning tasks by learning robust generalizable algorithms, or do they memorize training data? To investigate this question, we use arithmetic reasoning as a representative task. Using causal analysis, we identify a subset of the model (a circuit) that explains most of the model's behavior for basic arithmetic logic and examine its functionality. By zooming in on the level of individual circuit neurons, we discover a sparse set of important neurons that implement simple heuristics. Each heuristic identifies a numerical input pattern and outputs corresponding answers. We hypothesize that the combination of these heuristic neurons is the mechanism used to produce correct arithmetic answers. To test this, we categorize each neuron into several heuristic types-such as neurons that activate when an operand falls within a certain range-and find that the unordered combination of these heuristic types is the mechanism that explains most of the model's accuracy on arithmetic prompts. Finally, we demonstrate that this mechanism appears as the main source of arithmetic accuracy early in training. Overall, our experimental results across several LLMs show that LLMs perform arithmetic using neither robust algorithms nor memorization; rather, they rely on a "bag of heuristics".

Redundancies and correlations in the responses of sensory neurons seem to waste neural resources but can carry cues about structured stimuli and may help the brain to correct for response errors. To assess how the retina negotiates this tradeoff, we measured simultaneous responses from populations of ganglion cells presented with natural and artificial stimuli that varied greatly in correlation structure. We found that pairwise correlations in the retinal output remained similar across stimuli with widely different spatio-temporal correlations including white noise and natural movies. Meanwhile, purely spatial correlations tended to increase correlations in the retinal response. Responding to more correlated stimuli, ganglion cells had faster temporal kernels and tended to have stronger surrounds. These properties of individual cells, along with gain changes that opposed changes in effective contrast at the ganglion cell input, largely explained the similarity of pairwise correlations across stimuli where receptive field measurements were possible.

Why do neurons communicate through spikes? By definition, spikes are all-or-none neural events which occur at continuous times. In other words, spikes are on one side binary, existing or not without further details, and on the other can occur at any asynchronous time, without the need for a centralized clock. This stands in stark contrast to the analog representation of values and the discretized timing classically used in digital processing and at the base of modern-day neural networks. As neural systems almost systematically use this so-called event-based representation in the living world, a better understanding of this phenomenon remains a fundamental challenge in neurobiology in order to better interpret the profusion of recorded data. With the growing need for intelligent embedded systems, it also emerges as a new computing paradigm to enable the efficient operation of a new class of sensors and event-based computers, called neuromorphic, which could enable significant gains in computation time and energy consumption -- a major societal issue in the era of the digital economy and global warming. In this review paper, we provide evidence from biology, theory and engineering that the precise timing of spikes plays a crucial role in our understanding of the efficiency of neural networks.

Attending to what is relevant is fundamental to both the mammalian brain and modern machine learning models such as Transformers. Yet, determining relevance remains a core challenge, traditionally offloaded to learning algorithms like backpropagation. Inspired by recent cellular neurobiological evidence linking neocortical pyramidal cells to distinct mental states, this work shows how models (e.g., Transformers) can emulate high-level perceptual processing and awake thought (imagination) states to pre-select relevant information before applying attention. Triadic neuronal-level modulation loops among questions (Q), clues (keys, K), and hypotheses (values, V) enable diverse, deep, parallel reasoning chains at the representation level and allow a rapid shift from initial biases to refined understanding. This leads to orders-of-magnitude faster learning with significantly reduced computational demand (e.g., fewer heads, layers, and tokens), at an approximate cost of O(N), where N is the number of input tokens. Results span reinforcement learning (e.g., CarRacing in a high-dimensional visual setup), computer vision, and natural language question answering.

There is renewed interest in modeling and understanding the nervous system of the nematode Caenorhabditis elegans (C. elegans), as this small model system provides a path to bridge the gap between nervous system structure (connectivity) and function (physiology). However, existing physiology datasets, whether involving passive recording or stimulation, are in distinct formats, and connectome datasets require preprocessing before analysis can commence. Here we compile and homogenize datasets of neural activity and connectivity. Our neural activity dataset is derived from 11 C. elegans neuroimaging experiments, while our connectivity dataset is compiled from 9 connectome annotations based on 3 primary electron microscopy studies and 1 signal propagation study. Physiology datasets, collected under varying protocols, measure calcium fluorescence in labeled subsets of the worm's 300 neurons. Our preprocessing pipeline standardizes these datasets by consistently ordering labeled neurons and resampling traces to a common sampling rate, yielding recordings from approximately 900 worms and 250 uniquely labeled neurons. The connectome datasets, collected from electron microscopy reconstructions, represent the entire nervous system as a graph of connections. Our collection is accessible on HuggingFace, facilitating analysis of the structure-function relationship in biology using modern neural network architectures and enabling cross-lab and cross-animal comparisons.

Spiking Neural Networks (SNNs) have garnered significant attention as a central paradigm in neuromorphic computing, owing to their energy efficiency and biological plausibility. However, training deep SNNs has critically depended on explicit normalization schemes, leading to a trade-off between performance and biological realism. To resolve this conflict, we propose a normalization-free learning framework that incorporates lateral inhibition inspired by cortical circuits. Our framework replaces the traditional feedforward SNN layer with distinct excitatory (E) and inhibitory (I) neuronal populations that capture the key features of the cortical E-I interaction. The E-I circuit dynamically regulates neuronal activity through subtractive and divisive inhibition, which respectively control the excitability and gain of neurons. To stabilize end-to-end training of the biologically constrained SNNs, we propose two key techniques: E-I Init and E-I Prop. E-I Init is a dynamic parameter initialization scheme that balances excitatory and inhibitory inputs while performing gain control. E-I Prop decouples the backpropagation of the circuit from the forward pass, regulating gradient flow. Experiments across multiple datasets and network architectures demonstrate that our framework enables stable training of deep normalization-free SNNs with biological realism, achieving competitive performance. Therefore, our work not only provides a solution to training deep SNNs but also serves as a computational platform for further exploring the functions of E-I interaction in large-scale cortical computation. Code is available at https://github.com/vwOvOwv/DeepEISNN.

The structure of biological neural circuits-modular, hierarchical, and sparsely interconnected-reflects an efficient trade-off between wiring cost, functional specialization, and robustness. These principles offer valuable insights for artificial neural network (ANN) design, especially as networks grow in depth and scale. Sparsity, in particular, has been widely explored for reducing memory and computation, improving speed, and enhancing generalization. Motivated by systems neuroscience findings, we explore how patterns of functional connectivity in the mouse visual cortex-specifically, ensemble-to-ensemble communication, can inform ANN design. We introduce G2GNet, a novel architecture that imposes sparse, modular connectivity across feedforward layers. Despite having significantly fewer parameters than fully connected models, G2GNet achieves superior accuracy on standard vision benchmarks. To our knowledge, this is the first architecture to incorporate biologically observed functional connectivity patterns as a structural bias in ANN design. We complement this static bias with a dynamic sparse training (DST) mechanism that prunes and regrows edges during training. We also propose a Hebbian-inspired rewiring rule based on activation correlations, drawing on principles of biological plasticity. G2GNet achieves up to 75% sparsity while improving accuracy by up to 4.3% on benchmarks, including Fashion-MNIST, CIFAR-10, and CIFAR-100, outperforming dense baselines with far fewer computations.

Neurons in the brain are spatially organized such that neighbors on tissue often exhibit similar response profiles. In the human language system, experimental studies have observed clusters for syntactic and semantic categories, but the mechanisms underlying this functional organization remain unclear. Here, building on work from the vision literature, we develop TopoLM, a transformer language model with an explicit two-dimensional spatial representation of model units. By combining a next-token prediction objective with a spatial smoothness loss, representations in this model assemble into clusters that correspond to semantically interpretable groupings of text and closely match the functional organization in the brain's language system. TopoLM successfully predicts the emergence of the spatio-functional organization of a cortical language system as well as the organization of functional clusters selective for fine-grained linguistic features empirically observed in human cortex. Our results suggest that the functional organization of the human language system is driven by a unified spatial objective, and provide a functionally and spatially aligned model of language processing in the brain.

Large language models (LLMs) frequently generate hallucinations -- plausible but factually incorrect outputs -- undermining their reliability. While prior work has examined hallucinations from macroscopic perspectives such as training data and objectives, the underlying neuron-level mechanisms remain largely unexplored. In this paper, we conduct a systematic investigation into hallucination-associated neurons (H-Neurons) in LLMs from three perspectives: identification, behavioral impact, and origins. Regarding their identification, we demonstrate that a remarkably sparse subset of neurons (less than 0.1% of total neurons) can reliably predict hallucination occurrences, with strong generalization across diverse scenarios. In terms of behavioral impact, controlled interventions reveal that these neurons are causally linked to over-compliance behaviors. Concerning their origins, we trace these neurons back to the pre-trained base models and find that these neurons remain predictive for hallucination detection, indicating they emerge during pre-training. Our findings bridge macroscopic behavioral patterns with microscopic neural mechanisms, offering insights for developing more reliable LLMs.

Developing a general robot manipulation system capable of performing a wide range of tasks in complex, dynamic, and unstructured real-world environments has long been a challenging task. It is widely recognized that achieving human-like efficiency and robustness manipulation requires the robotic brain to integrate a comprehensive set of functions, such as task planning, policy generation, anomaly monitoring and handling, and long-term memory, achieving high-efficiency operation across all functions. Vision-Language Models (VLMs), pretrained on massive multimodal data, have acquired rich world knowledge, exhibiting exceptional scene understanding and multimodal reasoning capabilities. However, existing methods typically focus on realizing only a single function or a subset of functions within the robotic brain, without integrating them into a unified cognitive architecture. Inspired by a divide-and-conquer strategy and the architecture of the human brain, we propose FrankenBot, a VLM-driven, brain-morphic robotic manipulation framework that achieves both comprehensive functionality and high operational efficiency. Our framework includes a suite of components, decoupling a part of key functions from frequent VLM calls, striking an optimal balance between functional completeness and system efficiency. Specifically, we map task planning, policy generation, memory management, and low-level interfacing to the cortex, cerebellum, temporal lobe-hippocampus complex, and brainstem, respectively, and design efficient coordination mechanisms for the modules. We conducted comprehensive experiments in both simulation and real-world robotic environments, demonstrating that our method offers significant advantages in anomaly detection and handling, long-term memory, operational efficiency, and stability -- all without requiring any fine-tuning or retraining.

Recurrent neural networks (RNNs) in the brain and in silico excel at solving tasks with intricate temporal dependencies. Long timescales required for solving such tasks can arise from properties of individual neurons (single-neuron timescale, tau, e.g., membrane time constant in biological neurons) or recurrent interactions among them (network-mediated timescale). However, the contribution of each mechanism for optimally solving memory-dependent tasks remains poorly understood. Here, we train RNNs to solve N-parity and N-delayed match-to-sample tasks with increasing memory requirements controlled by N by simultaneously optimizing recurrent weights and taus. We find that for both tasks RNNs develop longer timescales with increasing N, but depending on the learning objective, they use different mechanisms. Two distinct curricula define learning objectives: sequential learning of a single-N (single-head) or simultaneous learning of multiple Ns (multi-head). Single-head networks increase their tau with N and are able to solve tasks for large N, but they suffer from catastrophic forgetting. However, multi-head networks, which are explicitly required to hold multiple concurrent memories, keep tau constant and develop longer timescales through recurrent connectivity. Moreover, we show that the multi-head curriculum increases training speed and network stability to ablations and perturbations, and allows RNNs to generalize better to tasks beyond their training regime. This curriculum also significantly improves training GRUs and LSTMs for large-N tasks. Our results suggest that adapting timescales to task requirements via recurrent interactions allows learning more complex objectives and improves the RNN's performance.

Some neurons in deep networks specialize in recognizing highly specific perceptual, structural, or semantic features of inputs. In computer vision, techniques exist for identifying neurons that respond to individual concept categories like colors, textures, and object classes. But these techniques are limited in scope, labeling only a small subset of neurons and behaviors in any network. Is a richer characterization of neuron-level computation possible? We introduce a procedure (called MILAN, for mutual-information-guided linguistic annotation of neurons) that automatically labels neurons with open-ended, compositional, natural language descriptions. Given a neuron, MILAN generates a description by searching for a natural language string that maximizes pointwise mutual information with the image regions in which the neuron is active. MILAN produces fine-grained descriptions that capture categorical, relational, and logical structure in learned features. These descriptions obtain high agreement with human-generated feature descriptions across a diverse set of model architectures and tasks, and can aid in understanding and controlling learned models. We highlight three applications of natural language neuron descriptions. First, we use MILAN for analysis, characterizing the distribution and importance of neurons selective for attribute, category, and relational information in vision models. Second, we use MILAN for auditing, surfacing neurons sensitive to human faces in datasets designed to obscure them. Finally, we use MILAN for editing, improving robustness in an image classifier by deleting neurons sensitive to text features spuriously correlated with class labels.

Sparse autoencoders have recently produced dictionaries of high-dimensional vectors corresponding to the universe of concepts represented by large language models. We find that this concept universe has interesting structure at three levels: 1) The "atomic" small-scale structure contains "crystals" whose faces are parallelograms or trapezoids, generalizing well-known examples such as (man-woman-king-queen). We find that the quality of such parallelograms and associated function vectors improves greatly when projecting out global distractor directions such as word length, which is efficiently done with linear discriminant analysis. 2) The "brain" intermediate-scale structure has significant spatial modularity; for example, math and code features form a "lobe" akin to functional lobes seen in neural fMRI images. We quantify the spatial locality of these lobes with multiple metrics and find that clusters of co-occurring features, at coarse enough scale, also cluster together spatially far more than one would expect if feature geometry were random. 3) The "galaxy" scale large-scale structure of the feature point cloud is not isotropic, but instead has a power law of eigenvalues with steepest slope in middle layers. We also quantify how the clustering entropy depends on the layer.

The Backpropagation algorithm, widely used to train neural networks, has often been criticised for its lack of biological realism. In an attempt to find a more biologically plausible alternative, and avoid to back-propagate gradients in favour of using local learning rules, the recently introduced Forward-Forward algorithm replaces the traditional forward and backward passes of Backpropagation with two forward passes. In this work, we show that internal representations obtained with the Forward-Forward algorithm organize into robust, category-specific ensembles, composed by an extremely low number of active units (high sparsity). This is remarkably similar to what is observed in cortical representations during sensory processing. While not found in models trained with standard Backpropagation, sparsity emerges also in networks optimized by Backpropagation, on the same training objective of Forward-Forward. These results suggest that the learning procedure proposed by Forward-Forward may be superior to Backpropagation in modelling learning in the cortex, even when a backward pass is used.

Spiking Neural Networks (SNNs) are well known as a promising energy-efficient alternative to conventional artificial neural networks. Subject to the preconceived impression that SNNs are sparse firing, the analysis and optimization of inherent redundancy in SNNs have been largely overlooked, thus the potential advantages of spike-based neuromorphic computing in accuracy and energy efficiency are interfered. In this work, we pose and focus on three key questions regarding the inherent redundancy in SNNs. We argue that the redundancy is induced by the spatio-temporal invariance of SNNs, which enhances the efficiency of parameter utilization but also invites lots of noise spikes. Further, we analyze the effect of spatio-temporal invariance on the spatio-temporal dynamics and spike firing of SNNs. Then, motivated by these analyses, we propose an Advance Spatial Attention (ASA) module to harness SNNs' redundancy, which can adaptively optimize their membrane potential distribution by a pair of individual spatial attention sub-modules. In this way, noise spike features are accurately regulated. Experimental results demonstrate that the proposed method can significantly drop the spike firing with better performance than state-of-the-art SNN baselines. Our code is available in https://github.com/BICLab/ASA-SNN.

Cortical circuits exhibit intricate recurrent architectures that are remarkably similar across different brain areas. Such stereotyped structure suggests the existence of common computational principles. However, such principles have remained largely elusive. Inspired by gated-memory networks, namely long short-term memory networks (LSTMs), we introduce a recurrent neural network in which information is gated through inhibitory cells that are subtractive (subLSTM). We propose a natural mapping of subLSTMs onto known canonical excitatory-inhibitory cortical microcircuits. Our empirical evaluation across sequential image classification and language modelling tasks shows that subLSTM units can achieve similar performance to LSTM units. These results suggest that cortical circuits can be optimised to solve complex contextual problems and proposes a novel view on their computational function. Overall our work provides a step towards unifying recurrent networks as used in machine learning with their biological counterparts.

The human brain is autonomously active, being characterized by a self-sustained neural activity which would be present even in the absence of external sensory stimuli. Here we study the interrelation between the self-sustained activity in autonomously active recurrent neural nets and external sensory stimuli. There is no a priori semantical relation between the influx of external stimuli and the patterns generated internally by the autonomous and ongoing brain dynamics. The question then arises when and how are semantic correlations between internal and external dynamical processes learned and built up? We study this problem within the paradigm of transient state dynamics for the neural activity in recurrent neural nets, i.e. for an autonomous neural activity characterized by an infinite time-series of transiently stable attractor states. We propose that external stimuli will be relevant during the sensitive periods, {\it viz} the transition period between one transient state and the subsequent semi-stable attractor. A diffusive learning signal is generated unsupervised whenever the stimulus influences the internal dynamics qualitatively. For testing we have presented to the model system stimuli corresponding to the bars and stripes problem. We found that the system performs a non-linear independent component analysis on its own, being continuously and autonomously active. This emergent cognitive capability results here from a general principle for the neural dynamics, the competition between neural ensembles.

We propose NEURONA, a neuro-symbolic framework for fMRI decoding and concept grounding in neural activity. Leveraging image- and video-based fMRI question-answering datasets, NEURONA learns to decode interacting concepts from visual stimuli based on patterns of fMRI responses, integrating symbolic reasoning and compositional execution with fMRI grounding across brain regions. We demonstrate that incorporating structural priors (e.g., compositional predicate-argument dependencies between concepts) into the decoding process significantly improves both decoding accuracy over precise queries, and notably, generalization to unseen queries at test time. With NEURONA, we highlight neuro-symbolic frameworks as promising tools for understanding neural activity.

Identifying cell types and understanding their functional properties is crucial for unraveling the mechanisms underlying perception and cognition. In the retina, functional types can be identified by carefully selected stimuli, but this requires expert domain knowledge and biases the procedure towards previously known cell types. In the visual cortex, it is still unknown what functional types exist and how to identify them. Thus, for unbiased identification of the functional cell types in retina and visual cortex, new approaches are needed. Here we propose an optimization-based clustering approach using deep predictive models to obtain functional clusters of neurons using Most Discriminative Stimuli (MDS). Our approach alternates between stimulus optimization with cluster reassignment akin to an expectation-maximization algorithm. The algorithm recovers functional clusters in mouse retina, marmoset retina and macaque visual area V4. This demonstrates that our approach can successfully find discriminative stimuli across species, stages of the visual system and recording techniques. The resulting most discriminative stimuli can be used to assign functional cell types fast and on the fly, without the need to train complex predictive models or show a large natural scene dataset, paving the way for experiments that were previously limited by experimental time. Crucially, MDS are interpretable: they visualize the distinctive stimulus patterns that most unambiguously identify a specific type of neuron.

We present a comprehensive analysis of how two-layer neural networks learn features to solve the modular addition task. Our work provides a full mechanistic interpretation of the learned model and a theoretical explanation of its training dynamics. While prior work has identified that individual neurons learn single-frequency Fourier features and phase alignment, it does not fully explain how these features combine into a global solution. We bridge this gap by formalizing a diversification condition that emerges during training when overparametrized, consisting of two parts: phase symmetry and frequency diversification. We prove that these properties allow the network to collectively approximate a flawed indicator function on the correct logic for the modular addition task. While individual neurons produce noisy signals, the phase symmetry enables a majority-voting scheme that cancels out noise, allowing the network to robustly identify the correct sum. Furthermore, we explain the emergence of these features under random initialization via a lottery ticket mechanism. Our gradient flow analysis proves that frequencies compete within each neuron, with the "winner" determined by its initial spectral magnitude and phase alignment. From a technical standpoint, we provide a rigorous characterization of the layer-wise phase coupling dynamics and formalize the competitive landscape using the ODE comparison lemma. Finally, we use these insights to demystify grokking, characterizing it as a three-stage process involving memorization followed by two generalization phases, driven by the competition between loss minimization and weight decay.

In theoretical neuroscience, recent work leverages deep learning tools to explore how some network attributes critically influence its learning dynamics. Notably, initial weight distributions with small (resp. large) variance may yield a rich (resp. lazy) regime, where significant (resp. minor) changes to network states and representation are observed over the course of learning. However, in biology, neural circuit connectivity could exhibit a low-rank structure and therefore differs markedly from the random initializations generally used for these studies. As such, here we investigate how the structure of the initial weights -- in particular their effective rank -- influences the network learning regime. Through both empirical and theoretical analyses, we discover that high-rank initializations typically yield smaller network changes indicative of lazier learning, a finding we also confirm with experimentally-driven initial connectivity in recurrent neural networks. Conversely, low-rank initialization biases learning towards richer learning. Importantly, however, as an exception to this rule, we find lazier learning can still occur with a low-rank initialization that aligns with task and data statistics. Our research highlights the pivotal role of initial weight structures in shaping learning regimes, with implications for metabolic costs of plasticity and risks of catastrophic forgetting.

The brain has computational capabilities that surpass those of modern systems, being able to solve complex problems efficiently in a simple way. Neuromorphic engineering aims to mimic biology in order to develop new systems capable of incorporating such capabilities. Bio-inspired learning systems continue to be a challenge that must be solved, and much work needs to be done in this regard. Among all brain regions, the hippocampus stands out as an autoassociative short-term memory with the capacity to learn and recall memories from any fragment of them. These characteristics make the hippocampus an ideal candidate for developing bio-inspired learning systems that, in addition, resemble content-addressable memories. Therefore, in this work we propose a bio-inspired spiking content-addressable memory model based on the CA3 region of the hippocampus with the ability to learn, forget and recall memories, both orthogonal and non-orthogonal, from any fragment of them. The model was implemented on the SpiNNaker hardware platform using Spiking Neural Networks. A set of experiments based on functional, stress and applicability tests were performed to demonstrate its correct functioning. This work presents the first hardware implementation of a fully-functional bio-inspired spiking hippocampal content-addressable memory model, paving the way for the development of future more complex neuromorphic systems.

Large language models (LLMs) exhibit strong multilingual abilities, yet the neural mechanisms behind language-specific processing remain unclear. We analyze language-specific neurons in Llama-3.1-8B, Mistral-Nemo-12B, and Aya-Expanse-8B & 32B across 21 typologically diverse languages, identifying neurons that control language behavior. Using the Language Activation Probability Entropy (LAPE) method, we show that these neurons cluster in deeper layers, with non-Latin scripts showing greater specialization. Related languages share overlapping neurons, reflecting internal representations of linguistic proximity. Through language arithmetics, i.e. systematic activation addition and multiplication, we steer models to deactivate unwanted languages and activate desired ones, outperforming simpler replacement approaches. These interventions effectively guide behavior across five multilingual tasks: language forcing, translation, QA, comprehension, and NLI. Manipulation is more successful for high-resource languages, while typological similarity improves effectiveness. We also demonstrate that cross-lingual neuron steering enhances downstream performance and reveal internal "fallback" mechanisms for language selection when neurons are progressively deactivated. Our code is made publicly available at https://github.com/d-gurgurov/Language-Neurons-Manipulation.

The performance of deep network learning strongly depends on the choice of the non-linear activation function associated with each neuron. However, deciding on the best activation is non-trivial, and the choice depends on the architecture, hyper-parameters, and even on the dataset. Typically these activations are fixed by hand before training. Here, we demonstrate how to eliminate the reliance on first picking fixed activation functions by using flexible parametric rational functions instead. The resulting Pad\'e Activation Units (PAUs) can both approximate common activation functions and also learn new ones while providing compact representations. Our empirical evidence shows that end-to-end learning deep networks with PAUs can increase the predictive performance. Moreover, PAUs pave the way to approximations with provable robustness. https://github.com/ml-research/pau

We can better understand deep neural networks by identifying which features each of their neurons have learned to detect. To do so, researchers have created Deep Visualization techniques including activation maximization, which synthetically generates inputs (e.g. images) that maximally activate each neuron. A limitation of current techniques is that they assume each neuron detects only one type of feature, but we know that neurons can be multifaceted, in that they fire in response to many different types of features: for example, a grocery store class neuron must activate either for rows of produce or for a storefront. Previous activation maximization techniques constructed images without regard for the multiple different facets of a neuron, creating inappropriate mixes of colors, parts of objects, scales, orientations, etc. Here, we introduce an algorithm that explicitly uncovers the multiple facets of each neuron by producing a synthetic visualization of each of the types of images that activate a neuron. We also introduce regularization methods that produce state-of-the-art results in terms of the interpretability of images obtained by activation maximization. By separately synthesizing each type of image a neuron fires in response to, the visualizations have more appropriate colors and coherent global structure. Multifaceted feature visualization thus provides a clearer and more comprehensive description of the role of each neuron.

A growing literature in computational neuroscience leverages gradient descent and learning algorithms that approximate it to study synaptic plasticity in the brain. However, the vast majority of this work ignores a critical underlying assumption: the choice of distance for synaptic changes - i.e. the geometry of synaptic plasticity. Gradient descent assumes that the distance is Euclidean, but many other distances are possible, and there is no reason that biology necessarily uses Euclidean geometry. Here, using the theoretical tools provided by mirror descent, we show that the distribution of synaptic weights will depend on the geometry of synaptic plasticity. We use these results to show that experimentally-observed log-normal weight distributions found in several brain areas are not consistent with standard gradient descent (i.e. a Euclidean geometry), but rather with non-Euclidean distances. Finally, we show that it should be possible to experimentally test for different synaptic geometries by comparing synaptic weight distributions before and after learning. Overall, our work shows that the current paradigm in theoretical work on synaptic plasticity that assumes Euclidean synaptic geometry may be misguided and that it should be possible to experimentally determine the true geometry of synaptic plasticity in the brain.

Labeling neural network submodules with human-legible descriptions is useful for many downstream tasks: such descriptions can surface failures, guide interventions, and perhaps even explain important model behaviors. To date, most mechanistic descriptions of trained networks have involved small models, narrowly delimited phenomena, and large amounts of human labor. Labeling all human-interpretable sub-computations in models of increasing size and complexity will almost certainly require tools that can generate and validate descriptions automatically. Recently, techniques that use learned models in-the-loop for labeling have begun to gain traction, but methods for evaluating their efficacy are limited and ad-hoc. How should we validate and compare open-ended labeling tools? This paper introduces FIND (Function INterpretation and Description), a benchmark suite for evaluating the building blocks of automated interpretability methods. FIND contains functions that resemble components of trained neural networks, and accompanying descriptions of the kind we seek to generate. The functions are procedurally constructed across textual and numeric domains, and involve a range of real-world complexities, including noise, composition, approximation, and bias. We evaluate new and existing methods that use language models (LMs) to produce code-based and language descriptions of function behavior. We find that an off-the-shelf LM augmented with only black-box access to functions can sometimes infer their structure, acting as a scientist by forming hypotheses, proposing experiments, and updating descriptions in light of new data. However, LM-based descriptions tend to capture global function behavior and miss local corruptions. These results show that FIND will be useful for characterizing the performance of more sophisticated interpretability methods before they are applied to real-world models.

The field of neuroscience and the development of artificial neural networks (ANNs) have mutually influenced each other, drawing from and contributing to many concepts initially developed in statistical mechanics. Notably, Hopfield networks and Boltzmann machines are versions of the Ising model, a model extensively studied in statistical mechanics for over a century. In the first part of this chapter, we provide an overview of the principles, models, and applications of ANNs, highlighting their connections to statistical mechanics and statistical learning theory. Artificial neural networks can be seen as high-dimensional mathematical functions, and understanding the geometric properties of their loss landscapes (i.e., the high-dimensional space on which one wishes to find extrema or saddles) can provide valuable insights into their optimization behavior, generalization abilities, and overall performance. Visualizing these functions can help us design better optimization methods and improve their generalization abilities. Thus, the second part of this chapter focuses on quantifying geometric properties and visualizing loss functions associated with deep ANNs.

This paper considers the Pointer Value Retrieval (PVR) benchmark introduced in [ZRKB21], where a 'reasoning' function acts on a string of digits to produce the label. More generally, the paper considers the learning of logical functions with gradient descent (GD) on neural networks. It is first shown that in order to learn logical functions with gradient descent on symmetric neural networks, the generalization error can be lower-bounded in terms of the noise-stability of the target function, supporting a conjecture made in [ZRKB21]. It is then shown that in the distribution shift setting, when the data withholding corresponds to freezing a single feature (referred to as canonical holdout), the generalization error of gradient descent admits a tight characterization in terms of the Boolean influence for several relevant architectures. This is shown on linear models and supported experimentally on other models such as MLPs and Transformers. In particular, this puts forward the hypothesis that for such architectures and for learning logical functions such as PVR functions, GD tends to have an implicit bias towards low-degree representations, which in turn gives the Boolean influence for the generalization error under quadratic loss.

Spiking neural networks (SNNs) are well suited for spatio-temporal learning and implementations on energy-efficient event-driven neuromorphic processors. However, existing SNN error backpropagation (BP) methods lack proper handling of spiking discontinuities and suffer from low performance compared with the BP methods for traditional artificial neural networks. In addition, a large number of time steps are typically required to achieve decent performance, leading to high latency and rendering spike-based computation unscalable to deep architectures. We present a novel Temporal Spike Sequence Learning Backpropagation (TSSL-BP) method for training deep SNNs, which breaks down error backpropagation across two types of inter-neuron and intra-neuron dependencies and leads to improved temporal learning precision. It captures inter-neuron dependencies through presynaptic firing times by considering the all-or-none characteristics of firing activities and captures intra-neuron dependencies by handling the internal evolution of each neuronal state in time. TSSL-BP efficiently trains deep SNNs within a much shortened temporal window of a few steps while improving the accuracy for various image classification datasets including CIFAR10.

A biological neural network in the cortex forms a neural field. Neurons in the field have their own receptive fields, and connection weights between two neurons are random but highly correlated when they are in close proximity in receptive fields. In this paper, we investigate such neural fields in a multilayer architecture to investigate the supervised learning of the fields. We empirically compare the performances of our field model with those of randomly connected deep networks. The behavior of a randomly connected network is investigated on the basis of the key idea of the neural tangent kernel regime, a recent development in the machine learning theory of over-parameterized networks; for most randomly connected neural networks, it is shown that global minima always exist in their small neighborhoods. We numerically show that this claim also holds for our neural fields. In more detail, our model has two structures: i) each neuron in a field has a continuously distributed receptive field, and ii) the initial connection weights are random but not independent, having correlations when the positions of neurons are close in each layer. We show that such a multilayer neural field is more robust than conventional models when input patterns are deformed by noise disturbances. Moreover, its generalization ability can be slightly superior to that of conventional models.

Transformer-based language models excel at both recall (retrieving memorized facts) and reasoning (performing multi-step inference), but whether these abilities rely on distinct internal mechanisms remains unclear. Distinguishing recall from reasoning is crucial for predicting model generalization, designing targeted evaluations, and building safer interventions that affect one ability without disrupting the other.We approach this question through mechanistic interpretability, using controlled datasets of synthetic linguistic puzzles to probe transformer models at the layer, head, and neuron level. Our pipeline combines activation patching and structured ablations to causally measure component contributions to each task type. Across two model families (Qwen and LLaMA), we find that interventions on distinct layers and attention heads lead to selective impairments: disabling identified "recall circuits" reduces fact-retrieval accuracy by up to 15\% while leaving reasoning intact, whereas disabling "reasoning circuits" reduces multi-step inference by a comparable margin. At the neuron level, we observe task-specific firing patterns, though these effects are less robust, consistent with neuronal polysemanticity.Our results provide the first causal evidence that recall and reasoning rely on separable but interacting circuits in transformer models. These findings advance mechanistic interpretability by linking circuit-level structure to functional specialization and demonstrate how controlled datasets and causal interventions can yield mechanistic insights into model cognition, informing safer deployment of large language models.

The abilities to perceive, learn, and use generalities, similarities, classes, i.e., semantic memory (SM), is central to cognition. Machine learning (ML), neural network, and AI research has been primarily driven by tasks requiring such abilities. However, another central facet of cognition, single-trial formation of permanent memories of experiences, i.e., episodic memory (EM), has had relatively little focus. Only recently has EM-like functionality been added to Deep Learning (DL) models, e.g., Neural Turing Machine, Memory Networks. However, in these cases: a) EM is implemented as a separate module, which entails substantial data movement (and so, time and power) between the DL net itself and EM; and b) individual items are stored localistically within the EM, precluding realizing the exponential representational efficiency of distributed over localist coding. We describe Sparsey, an unsupervised, hierarchical, spatial/spatiotemporal associative memory model differing fundamentally from mainstream ML models, most crucially, in its use of sparse distributed representations (SDRs), or, cell assemblies, which admits an extremely efficient, single-trial learning algorithm that maps input similarity into code space similarity (measured as intersection). SDRs of individual inputs are stored in superposition and because similarity is preserved, the patterns of intersections over the assigned codes reflect the similarity, i.e., statistical, structure, of all orders, not simply pairwise, over the inputs. Thus, SM, i.e., a generative model, is built as a computationally free side effect of the act of storing episodic memory traces of individual inputs, either spatial patterns or sequences. We report initial results on MNIST and on the Weizmann video event recognition benchmarks. While we have not yet attained SOTA class accuracy, learning takes only minutes on a single CPU.